المؤلفون: Tkachuk, Vladimir V.

مصطلحات موضوعية: keyword:Lindelöf space, keyword:scattered space, keyword:$\sigma$-product, keyword:function space, keyword:$P$-space, keyword:exponentially separable space, keyword:product, keyword:functionally countable space, keyword:weakly exponentially separable space, msc:54C35, msc:54D65, msc:54G10, msc:54G12

وصف الملف: application/pdf

Relation: mr:MR4542797; zbl:Zbl 07655808; reference:[1] Engelking R.: General Topology.Mathematical Monographs, 60, PWN—Polish Scientific Publishers, Warszawa, 1977. Zbl 0684.54001, MR 0500780; reference:[2] Galvin F.: Problem 6444.Amer. Math. Monthly 90 (1983), no. 9, 648; solution: Amer. Math. Monthly 92 (1985), no. 6, 434. MR 1540672; reference:[3] Gruenhage G., Tkachuk V. V., Wilson R. G.: Domination by small sets versus density.Topology Appl. 282 (2020), 107306, 10 pages. MR 4116835, 10.1016/j.topol.2020.107306; reference:[4] Juhász I., van Mill J.: Countably compact spaces all countable subsets of which are scattered.Comment. Math. Univ. Carolin. 22 (1981), no. 4, 851–855. MR 0647031; reference:[5] Levy R., Matveev M.: Functional separability.Comment. Math. Univ. Carolin. 51 (2010), no. 4, 705–711. Zbl 1224.54063, MR 2858271; reference:[6] Moore J. T.: A solution to the $L$ space problem.J. Amer. Math. Soc. 19 (2006), no. 3, 717–736. Zbl 1107.03056, MR 2220104, 10.1090/S0894-0347-05-00517-5; reference:[7] Pelczyński A., Semadeni Z.: Spaces of continuous functions. III. Spaces $C(\Omega)$ for $\Omega$ without perfect subsets.Studia Math. 18 (1959), 211–222. MR 0107806, 10.4064/sm-18-2-211-222; reference:[8] Rudin W.: Continuous functions on compact spaces without perfect subsets.Proc. Amer. Math. Soc. 8 (1957), 39–42. Zbl 0077.31103, MR 0085475, 10.1090/S0002-9939-1957-0085475-7; reference:[9] Tkachuk V. V.: A $C_p$-Theory Problem Book. Topological and Function Spaces.Problem Books in Mathematics, Springer, New York, 2011. MR 3024898; reference:[10] Tkachuk V. V.: A $C_p$-Theory Problem Book. Special Features of Function Spaces.Problem Books in Mathematics, Springer, Cham, 2014. MR 3243753; reference:[11] Tkachuk V. V.: A $C_p$-Theory Problem Book. Compactness in Function Spaces.Problem Books in Mathematics, Springer, Cham, 2015. MR 3364185; reference:[12] Tkachuk V. V.: A nice subclass of functionally countable spaces.Comment. Math. Univ. Carolin. 59 (2018), no. 3, 399–409. MR 3861562; reference:[13] Tkachuk V. V.: Exponential domination in function spaces.Comment. Math. Univ. Carolin. 61 (2020), no. 3, 397–408. MR 4186115; reference:[14] Tkachuk V. V.: Some applications of discrete selectivity and Banakh property in function spaces.Eur. J. Math. 6 (2020), no. 1, 88–97. MR 4071459, 10.1007/s40879-019-00342-7; reference:[15] Tkachuk V. V.: Some applications of exponentially separable spaces.Quaest. Math. 43 (2020), no. 10, 1391–1403. MR 4175405, 10.2989/16073606.2019.1623934; reference:[16] Tkachuk V. V.: The extent of a weakly exponentially separable space can be arbitrarily large.Houston J. Math. 46 (2020), no. 3, 809–819. MR 4229084; reference:[17] Vaughan J. E.: Countably compact and sequentially compact spaces.Handbook of Set-Theoretic Topology, North Holland, Amsterdam, 1984, pages 569–602. Zbl 0562.54031, MR 0776631

الاتاحة: http://hdl.handle.net/10338.dmlcz/151541

المؤلفون: Tkachuk, Vladimir V.

مصطلحات موضوعية: keyword:countably compact space, keyword:Lindelöf space, keyword:Lindelöf $P$-space, keyword:functionally countable space, keyword:exponentially separable space, keyword:retraction, keyword:scattered space, keyword:extent, keyword:Sokolov space, keyword:weakly Sokolov space, keyword:function space, msc:54C35, msc:54D65, msc:54G10, msc:54G12

وصف الملف: application/pdf

Relation: mr:MR3861562; zbl:Zbl 06940880; reference:[1] Engelking R.: General Topology.Mathematical Monographs, 60, Polish Scientific Publishers, Warsaw, 1977. Zbl 0684.54001, MR 0500780; reference:[2] Kannan V., Rajagopalan M.: Scattered spaces II.Illinois J. Math. 21 (1977), no. 4, 735–751. MR 0474180; reference:[3] Moore J. T.: A solution to the $L$ space problem.J. Amer. Math. Soc. 19 (2006), no. 3, 717–736. Zbl 1107.03056, MR 2220104, 10.1090/S0894-0347-05-00517-5; reference:[4] Mrówka S.: Some set-theoretic constructions in topology.Fund. Math. 94 (1977), no. 2, 83–92. MR 0433388, 10.4064/fm-94-2-83-92; reference:[5] Rojas-Hernández R., Tkachuk V. V.: A monotone version of the Sokolov property and monotone retractability in function spaces.J. Math. Anal. Appl. 412 (2014), no. 1, 125–137. MR 3145787, 10.1016/j.jmaa.2013.10.043; reference:[6] Sokolov G. A.: Lindelöf spaces of continuous functions.Matem. Zametki 39 (1986), no. 6, 887–894, 943 (Russian). MR 0855936; reference:[7] Telgársky R.: Spaces defined by topological games.Fund. Math. 88 (1975), no. 3, 193–223. MR 0380708, 10.4064/fm-88-3-193-223; reference:[8] Tkachuk V. V.: A nice class extracted from $C_p$-theory.Comment. Math. Univ. Carolin. 46 (2005), no. 3, 503–513. MR 2174528; reference:[9] Tkachuk V. V.: A $C_p$-theory Problem Book. Topological and Function Spaces.Problem Books in Mathematics, Springer, New York, 2011. Zbl 1222.54002, MR 3024898; reference:[10] Tkachuk V. V.: A $C_p$-theory Problem Book. Special Features of Function Spaces.Problem Books in Mathematics, Springer, Cham, 2014. MR 3243753; reference:[11] Tkachuk V. V.: A $C_p$-theory Problem Book. Compactness in Function Spaces.Problem Books in Mathematics, Springer, Cham, 2015. MR 3364185; reference:[12] Tkachuk V. V.: Lindelöf $P$-spaces need not be Sokolov.Math. Slovaca 67 (2017), no. 1, 227–234. MR 3630168, 10.1515/ms-2016-0262; reference:[13] Uspenskij V. V.: On the spectrum of frequencies of function spaces.Vestnik Moskov. Univ. Ser. I Mat. Mekh. 37 (1982), no. 1, 31–35 (Russian. English summary). MR 0650600

الاتاحة: http://hdl.handle.net/10338.dmlcz/147407

المؤلفون: Keremedis, Kyriakos

مصطلحات موضوعية: keyword:axiom of choice, keyword:compact space, keyword:countably compact space, keyword:totally bounded space, keyword:Lindelöf space, keyword:separable space, keyword:second countable metric space, msc:54E35, msc:54E45

وصف الملف: application/pdf

Relation: mr:MR3783812; zbl:Zbl 06890400; reference:[1] Bentley H. L., Herrlich H.: Countable choice and pseudometric spaces.Topology Appl. 85 (1998), 153–164. Zbl 0922.03068, 10.1016/S0166-8641(97)00138-7; reference:[2] Brunner N.: Lindelöf Räume und Auswahlaxiom.Anz. Österr. Akad. Wiss. Math.-Nat. 119 (1982), 161–165.; reference:[3] Good C., Tree I. J., Watson S.: On Stone's theorem and the axiom of choice.Proc. Amer. Math. Soc. 126 (1998), 1211–1218. 10.1090/S0002-9939-98-04163-X; reference:[4] Herrlich H.: Axiom of Choice.Lecture Notes in Mathematics, 1876, Springer, Berlin, 2006. Zbl 1102.03049; reference:[5] Herrlich H.: Products of Lindelöf $T_{2}$-spaces are Lindelöf---in some models of $ {\rm {ZF}}$.Comment. Math. Univ. Carolin. 43, (2002), no. 2, 319–333.; reference:[6] Herrlich H., Strecker G. E.: When is $\mathbb N$ Lindelöf?.Comment. Math. Univ. Carolin. 38 (1997), no. 3, 553–556.; reference:[7] Howard P., Keremedis K., Rubin J. E., Stanley A.: Paracompactness of metric spaces and the axiom of multiple choice.Math. Log. Q. 46 (2000), no. 2, 219–232. 10.1002/(SICI)1521-3870(200005)46:23.0.CO;2-2; reference:[8] Howard P., Rubin J. E.: Consequences of the Axiom of Choice.Math. Surveys and Monographs, 59, American Mathematical Society, Providence, 1998. Zbl 0947.03001, 10.1090/surv/059; reference:[9] Keremedis K.: On the relative strength of forms of compactness of metric spaces and their countable productivity in $\mathbf {ZF}$.Topology Appl. 159 (2012), 3396–3403. 10.1016/j.topol.2012.08.003; reference:[10] Keremedis K.: On metric spaces where continuous real valued functions are uniformly continuous in $\mathbf {ZF}$.Topology Appl. 210 (2016), 366–375. 10.1016/j.topol.2016.07.021; reference:[11] Keremedis K.: Some notions of separability of metric spaces in $\mathbf {ZF}$ and their relation to compactness.Bull. Polish Acad. Sci. Math. 64 (2016), 109–136. 10.4064/ba8087-12-2016; reference:[12] Keremedis K., Tachtsis E.: Compact metric spaces and weak forms of the axiom of choice.MLQ Math. Log. Q. 47 (2001), 117–128. 10.1002/1521-3870(200101)47:13.0.CO;2-N; reference:[13] Munkres J. R.: Topology.Prentice-Hall, New Jersey, 1975. Zbl 0951.54001; reference:[14] Tachtsis E.: Disasters in metric topology without choice.Comment. Math. Univ. Carolin. 43 (2002), no. 1, 165–174.

الاتاحة: http://hdl.handle.net/10338.dmlcz/147182

المؤلفون: Hager, Anthony W.

مصطلحات موضوعية: keyword:real-valued function, keyword:Stone-Weierstrass, keyword:uniform approximation, keyword:Lindelöf space, keyword:locally in, msc:06F20, msc:26E99, msc:41A30, msc:46E05, msc:54C30, msc:54C35, msc:54D20, msc:54D35

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الاتاحة: http://hdl.handle.net/10338.dmlcz/141501

المؤلفون: Song, Yankui

مصطلحات موضوعية: keyword:Lindelöf space, keyword:strongly Lindelöf subset, keyword:almost Lindelöf subset, keyword:strongly almost Lindelöf subset, msc:54D15, msc:54D20

وصف الملف: application/pdf

Relation: mr:MR2535146; zbl:Zbl 1212.54079; reference:[1] Arhangel'skii, A. V., Hamdi, M. M., Genedi: The beginnings of the theory of relative topological properties.General Topology. Spaces and Functions, MGU, Moskva (1989), 3-48 Russian.; reference:[2] Arhangel'skii, A. V.: A generic theorem in the theory of cardinal invariants of topological spaces.Comment. Math. Univ. Carolinae 36 (1995), 303-325. MR 1357532; reference:[3] Engelking, R.: General Topology.Revised and completed edition, Heldermann (1989). Zbl 0684.54001, MR 1039321; reference:[4] Kočinac, Lj. D.: Some relative topological properties.Mat. Vesn. 44 (1992), 33-44. MR 1201265; reference:[5] Cammaroto, F., Santoro, G.: Some counterexamples and properties on generalizations of Lindelöf spaces.Int. J. Math. Math. Sci. 19 (1996), 737-746. Zbl 0860.54033, MR 1397840, 10.1155/S0161171296001020; reference:[6] Willard, S., Dissanayake, U. N. B.: The almost Lindelöf degree.Can. Math. Bull. 27 (1984), 452-455. Zbl 0551.54003, MR 0763044, 10.4153/CMB-1984-070-2

الاتاحة: http://hdl.handle.net/10338.dmlcz/140653

المؤلفون: Song, Yan-Kui

مصطلحات موضوعية: keyword:compact space, keyword:countably compact space, keyword:Lindelöf space, keyword:$\Cal K$-starcompact space, keyword:$\Cal C$-starcompact space, keyword:$\Cal L$-starcompact space, msc:54D20, msc:54D55

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140616

المؤلفون: Arhangel'skii, A. V.

مصطلحات موضوعية: keyword:remainder, keyword:compactification, keyword:topological group, keyword:$p$-space, keyword:Lindelöf $p$-space, keyword:metrizability, keyword:countable type, keyword:Lindelöf space, keyword:pseudocompact space, keyword:$\pi $-base, msc:54A25, msc:54B05

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Relation: mr:MR2433629; zbl:Zbl 1212.54086; reference:[1] Arhangel'skii A.V.: On a class of spaces containing all metric and all locally compact spaces.Mat. Sb. 67 (109) (1965), 55-88; English translation: Amer. Math. Soc. Transl. 92 (1970), 1-39. MR 0190889; reference:[2] Arhangel'skii A.V.: Classes of topological groups.Russian Math. Surveys 36 (3) (1981), 151-174. MR 0622722, 10.1070/RM1981v036n03ABEH004249; reference:[3] Arhangel'skii A.V.: Some connections between properties of topological groups and of their remainders.Moscow Univ. Math. Bull. 54:3 (1999), 1-6. MR 1711899; reference:[4] Arhangel'skii A.V.: Topological invariants in algebraic environment.in: Recent Progress in General Topology 2, eds. M. Hušek, Jan van Mill, North-Holland, Amsterdam, 2002, pp.1-57. Zbl 1030.54026, MR 1969992; reference:[5] Arhangel'skii A.V.: Remainders in compactifications and generalized metrizability properties.Topology Appl. 150 (2005), 79-90. Zbl 1075.54012, MR 2133669, 10.1016/j.topol.2004.10.015; reference:[6] Arhangel'skii A.V.: More on remainders close to metrizable spaces.Topology Appl. 154 (2007), 1084-1088. Zbl 1144.54001, MR 2298623, 10.1016/j.topol.2006.10.008; reference:[7] Engelking R.: General Topology.PWN, Warszawa, 1977. Zbl 0684.54001, MR 0500780; reference:[8] Filippov V.V.: On perfect images of paracompact $p$-spaces.Soviet Math. Dokl. 176 (1967), 533-536. MR 0222853; reference:[9] Henriksen M., Isbell J.R.: Some properties of compactifications.Duke Math. J. 25 (1958), 83-106. Zbl 0081.38604, MR 0096196, 10.1215/S0012-7094-58-02509-2; reference:[10] Tkachenko M.G.: The Suslin property in free topological groups over compact spaces (Russian).Mat. Zametki 34 (1983), 601-607; English translation: Math. Notes 34 (1983), 790-793. MR 0722229; reference:[11] Roelke W., Dierolf S.: Uniform Structures on Topological Groups and their Quotients.McGraw-Hill, New York, 1981.

الاتاحة: http://hdl.handle.net/10338.dmlcz/119706

المؤلفون: Boulabiar, Karim

مصطلحات موضوعية: keyword:algebra of real-valued functions, keyword:evaluating linear functional, keyword:homomorphism, keyword:Lindelöf space, msc:46E25, msc:54C35

وصف الملف: application/pdf

Relation: mr:MR2462976; zbl:Zbl 1212.46055; reference:[1] Biström, P., Bjon, S., Lindström, M.: Remarks on homomorphisms on certain subalgebras of $C( X) $.Math. Japon. 37 (1992), 105–109. Zbl 0798.46016, MR 1148522; reference:[2] Blasco, J. L.: On the structure of positive homomorphisms on algebras of real-valued functions.Acta Math. Hungar. 102 (2004), 141–150. MR 2038174, 10.1023/B:AMHU.0000023212.91183.38; reference:[3] Bonsall, F. F., Duncan, J.: Complete Normed Algebras.Springer Verlag, Berlin–Heidelberg–New York, 1973. Zbl 0271.46039, MR 0423029; reference:[4] Garrido, I., Gómez, J., Jaramillo, J.: Homomorphisms on functions algebras.Canad. J. Math. 46 (1994), 734–745. MR 1289057, 10.4153/CJM-1994-041-3; reference:[5] Gillman, L., Jerison, M.: Rings of Continuous Functions.Springer Verlag, Berlin–Heidelberg–New York, 1976. Zbl 0327.46040, MR 0407579; reference:[6] Isbell, J.: Algebra of uniformly continuous functions.Ann. Math. 68 (1958), 96–125. MR 0103407, 10.2307/1970045; reference:[7] Kriegl, A., Michor, P. W.: The Convenient Setting of Global Analysis.Math. Surveys Monogr., 1997. Zbl 0889.58001, MR 1471480; reference:[8] Steen, L. A., Seebach, J. A.: Counterexamples in Topology.Springer Verlag, Berlin–Heidelberg–New York, 1978. Zbl 0386.54001, MR 0507446

الاتاحة: http://hdl.handle.net/10338.dmlcz/119760

المؤلفون: Buzyakova, R. Z., Tkachuk, V. V., Wilson, R. G.

مصطلحات موضوعية: keyword:neighbourhood assignment, keyword:duality, keyword:weak duality, keyword:Lindelöf space, keyword:weakly Lindelöf space, msc:22A05, msc:54C10, msc:54C25, msc:54D06, msc:54D20, msc:54D25, msc:54H11

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الاتاحة: http://hdl.handle.net/10338.dmlcz/119691

المؤلفون: Buzyakova, Raushan Z.

مصطلحات موضوعية: keyword:$C_p(X)$, keyword:space of ordinals, keyword:Lindelöf space, msc:54C35, msc:54D20, msc:54F05

وصف الملف: application/pdf

Relation: mr:MR2076866; zbl:Zbl 1098.54010; reference:[ARH] Arhangelskii A.: Topological Function Spaces.Math. Appl., vol. 78, Kluwer Academic Publisher, Dordrecht, 1992. MR 1144519; reference:[ASA] Asanov M.O.: On cardinal invariants of function spaces.Modern Topology and Set Theory, Igevsk, (2), 1979, 8-12.; reference:[BAT] Baturov D.: On subspaces of function spaces.Vestnik MGU, Mat. Mech. 4 (1987), 66-69. Zbl 0665.54004, MR 0913076; reference:[BUZ] Buzyakova R.: Hereditary D-property of Function Spaces Over Compacta.submitted to Proc. Amer. Math. Soc. Zbl 1064.54029, MR 2073321; reference:[DOU] van Douwen E.K.: Simultaneous extension of continuous functions.Thesis, Free University, Amsterdam, 1975.; reference:[ENG] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl 0684.54001, MR 1039321; reference:[NAH] Nahmanson L.B.: Lindelöfness in function spaces.Fifth Teraspol Symposium on Topology and its Applications, Kishinev, 1985, p.183.

الاتاحة: http://hdl.handle.net/10338.dmlcz/119443

المؤلفون: Arhangel'skii, A. V., Buzyakova, R. Z.

مصطلحات موضوعية: keyword:$D$-space, keyword:point-countable base, keyword:extent, keyword:metrizable space, keyword:Lindelöf space, msc:54D20, msc:54E35, msc:54F99

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/119354

المؤلفون: Arhangel'skii, A. V., Pavlov, O. I.

مصطلحات موضوعية: keyword:condensation, keyword:compactum, keyword:network, keyword:Lindelöf space, keyword:topology of pointwise convergence, keyword:$\sigma $-compact space, keyword:Eberlein compactum, keyword:Corson compactum, keyword:Borel set, keyword:monolithic space, keyword:tightness, msc:54A25, msc:54A35, msc:54C35, msc:54D30

وصف الملف: application/pdf

Relation: mr:MR1920523; zbl:Zbl 1090.54003; reference:[1] Arhangelskii A.V.: Continuous maps, factorization theorems, and function spaces.Trans. Moscow Math. Soc. 47 (1985), 1-22.; reference:[2] Arhangelskii A.V.: Topological Function Spaces.Kluwer Academic Publishers, Dordrecht, 1992, p. 205. MR 1144519; reference:[3] Arhangelskii A.V.: $C_p$-theory.pp.1-56 in: M. Hu\u sek and J. van Mill, Eds, Recent Progress in General Topology, North-Holland, Amsterdam-London-New-York, 1992, 796 pp.; reference:[4] Arhangelskii A.V.: On condensations of $C_p$-spaces onto compacta.Proc. Amer. Math. Soc. 128 (2000), 1881-1883. MR 1751998; reference:[5] Arhangelskii A.V., Ponomarev V.I.: Fundamentals of General Topology in Problems and Exercises.D. Reidel Publ. Co., Dordrecht-Boston, Mass., 1984. MR 0785749; reference:[6] Banach S.: Livre Ecossais.Problem 1, 17:8, 1935; Colloq. Math. 1 (1947), p.150.; reference:[7] Dobrowolski T., Marciszewski W.: Classification of function spaces with the topology determined by a countable dense set.Fund. Math. 148 (1995), 35-62. MR 1354937; reference:[8] Godefroy G.: Compacts de Rosenthal.Pacific J. Math. 91 (1980), 293-306. Zbl 0475.46003, MR 0615679; reference:[9] Juhasz I.: Cardinal functions in topology.Math. Centre Tracts 34, Amsterdam, 1971. Zbl 0479.54001, MR 0340021; reference:[10] Marciszewski W.: A function space $C_p(X)$ without a condensation onto a $\sigma $-compact space.submitted, 2001. Zbl 1019.54012; reference:[11] Marciszewski W.: On a classification of pointwise compact sets of the first Baire class functions.Fund. Math. 133 (1989), 195-209. Zbl 0719.54022, MR 1065902; reference:[12] Pytkeev E.G.: Upper bounds of topologies.Math. Notes 20:4 (1976), 831-837. MR 0428237; reference:[13] Tkachenko M.G.: Bicompacta that are continuous images of sets everywhere dense in the product of spaces.Bull. Acad. Polon. Sci. Ser. Sci. Math. 27:10 (1979), 797-802. MR 0603151; reference:[14] Tkachenko M.G.: On continuous images of spaces of functions.Siberian Math. J. 26:5 (1985), 159-167. MR 0808711; reference:[15] Tkachenko M.G.: Factorization theorems for topological groups and their applications.Topology Appl. 38 (1991), 21-37. Zbl 0722.54039, MR 1093863; reference:[16] Tkachenko M.G.: On continuous images of dense subspaces of topological products.Uspekhi Mat. Nauk 34:6 (1979), 199-202. MR 0562841

الاتاحة: http://hdl.handle.net/10338.dmlcz/119337

المؤلفون: Herrlich, Horst

مصطلحات موضوعية: keyword:axiom of choice, keyword:axiom of countable choice, keyword:Lindelöf space, keyword:compact space, keyword:product, keyword:sum, msc:03E25, msc:54A35, msc:54B10, msc:54D20, msc:54D30

وصف الملف: application/pdf

Relation: mr:MR1922130; zbl:Zbl 1072.03029; reference:[1] Bentley H.L., Herrlich H.: Countable choice and pseudometric spaces.Topology Appl. 85 (1998), 153-164. Zbl 0922.03068, MR 1617460; reference:[2] Börger R.: On powers of a Lindelöf space.preprint, November 2001.; reference:[3] Brunner N.: $\sigma$-kompakte Räume.Manuscripta Math. 38 (1982), 375-379. Zbl 0504.54004, MR 0667922; reference:[4] Brunner N.: Lindelöf Räume und Auswahlaxiom.Anz. Österreich. Akad. der Wiss. Math. Nat. Kl. 119 (1982), 161-165. MR 0728812; reference:[5] Brunner N.: Spaces of Urelements, II.Rend. Sem. Mat. Univ. Padova 77 (1987), 305-315. Zbl 0668.54014, MR 0904626; reference:[6] Church A.: Alternatives to Zermelo's assumption.Trans. Amer. Math. Soc. 29 (1927), 178-208. MR 1501383; reference:[7] Engelking R.: General Topology.Heldermann Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321; reference:[8] Feferman S., Levy A.: Independence results in set theory by Cohen's method.Notices Amer. Math. Soc. 10 (1963), 593.; reference:[9] Gitik M.: All uncountable cardinals can be singular.Israel J. Math. 35 (1980), 61-88. Zbl 0439.03036, MR 0576462; reference:[10] Good C., Tree I.J.: Continuing horrors of topology without choice.Topology Appl. 63 (1995), 79-90. Zbl 0822.54001, MR 1328621; reference:[11] Gutierres G.: Sequential topological conditions without AC.preprint, 2001.; reference:[12] Herrlich H.: Compactness and the axiom of choice.Appl. Categ. Structures 3 (1995), 1-15. MR 1393958; reference:[13] Herrlich H., Keremedis K.: On countable products of finite Hausdorff spaces.Math. Logic Quart. 46 (2000), 537-542. Zbl 0959.03033, MR 1791548; reference:[14] Herrlich H., Strecker G.E.: When is $\Bbb N$ Lindelöf?.Comment. Math. Univ. Carolinae 38 (1997), 553-556. Zbl 0938.54008, MR 1485075; reference:[15] Howard P., Rubin J.E.: Consequences of the Axiom of Choice.AMS Math. Surveys and Monographs 59 AMS, Providence, RI, 1998. Zbl 0947.03001, MR 1637107; reference:[16] Jech T.J.: The Axiom of Choice.North-Holland, Amsterdam, 1973. Zbl 0259.02052, MR 0396271; reference:[17] Kelley J.: The Tychonoff product theorem implies the axiom of choice.Fund. Math. 37 (1950), 75-76. Zbl 0039.28202, MR 0039982; reference:[18] Keremedis K.: Disasters in topology without the axiom of choice.Arch. Math. Logic, 2000, to appear. Zbl 1027.03040, MR 1867681; reference:[19] Keremedis K.: Countable disjoint unions in topology and some weak forms of the axiom of choice.Arch. Math. Logic, submitted.; reference:[20] Keremedis K., Tachtsis E.: On Lindelöf metric spaces and weak forms of the axiom of choice.Math. Logic Quart. 46 (2000), 35-44. Zbl 0952.03060, MR 1736648; reference:[21] Lindelöf E.: Sur quelques points de la théorie des ensembles.C.R. Acad. Paris 137 (1903), 697-700.; reference:[22] Mycielski J., Steinhaus H.: A mathematical axiom contradicting the axiom of choice.Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 10 (1962), 1-3. Zbl 0106.00804, MR 0140430; reference:[23] Rhineghost Y.T.: The naturals are Lindelöf iff Ascoli holds.Categorical Perspectives (eds. J. Koslowski and A. Melton), Birkhäuser, 2001. Zbl 0983.03039, MR 1827669; reference:[24] Rubin H., Scott D.: Some topological theorems equivalent to the Boolean prime ideal theorem.Bull. Amer. Math. Soc. 60 (1954), 389.; reference:[25] Sageev G.: An independence result concerning the axiom of choice.Annals Math. Logic 8 (1975), 1-184. Zbl 0306.02060, MR 0366668; reference:[26] Specker E.: Zur Axiomatik der Mengenlehre (Fundierungs- und Auswahlaxiom).Z. Math. Logik Grundlagen Math. 3 (1957), 173-210. Zbl 0079.07605, MR 0099297; reference:[27] van Douwen E.K.: Horrors of topology without AC: a nonnormal orderable space.Proc. Amer. Math. Soc. 95 (1985), 101-105. Zbl 0574.03039, MR 0796455

الاتاحة: http://hdl.handle.net/10338.dmlcz/119322

المؤلفون: Arhangel'skii, A. V.

مصطلحات موضوعية: keyword:extremally disconnected, keyword:semitopological group, keyword:order 2, keyword:Souslin number, keyword:Lindelöf space, msc:54A25, msc:54C05, msc:54G05, msc:54G15, msc:54H11

وصف الملف: application/pdf

Relation: mr:MR1800164; zbl:Zbl 1049.54033; reference:[1] Arhangel'skii A.V.: Groupes topologiques extremalement discontinus.C.R. Acad. Sci. Paris 265 (1967), 822-825. MR 0222207; reference:[2] Arhangel'skii A.V., Ponomarev V.I.: Fundamentals of General Topology: Problems and Exercises.Reidel, 1984. MR 0785749; reference:[3] Efimov B.A.: Absolutes of homogeneous spaces.Dokl. Akad. Nauk SSSR 179:2 (1968), 271-274. Zbl 0179.27802, MR 0227937; reference:[4] Frolík Z.: Fixed points of maps of extremally disconnected spaces and complete Boolean Algebras.Bull. Acad. Polon. Sci., Ser. Math., Astronom., Phys. 16 (1968), 269-275. MR 0233343; reference:[5] Frolík Z.: Fixed points of maps of $\beta N$.Bull. Amer. Math. Soc. 74 (1968), 187-191. MR 0222847; reference:[6] Frolík Z.: Maps of extremally disconnected spaces, theory of types, and applications.General Topology and its Relations to Modern Analysis and Algebra, 3. (Proc. Conf., Kanpur, 1968), pp.131-142; Academia, Prague, 1971. MR 0295305; reference:[7] Katětov M.: A theorem on mappings.Comment. Math. Univ. Carolinae 8:3 (1967), 431-433. MR 0229228; reference:[8] Malychin V.I.: Extremally disconnected and close to them groups.Dokl. Akad. Nauk SSSR 220:1 (1975), 27-30. MR 0382536; reference:[9] Raimi R.: Homeomorphisms and invariant measures for $\beta N\setminus N$.Duke Math. J. 33 (1966), 1-12. MR 0198450; reference:[10] Sirota S.: Products of topological groups and extremal disconnectedness.Matem. Sb. 79:2 (1969), 179-192. MR 0242988

الاتاحة: http://hdl.handle.net/10338.dmlcz/119211

المؤلفون: Herrlich, Horst, Strecker, George E.

مصطلحات موضوعية: keyword:axiom of choice, keyword:axiom of countable choice, keyword:Lindelöf space, keyword:separable space, keyword:(sequential) continuity, keyword:(Dedekind-) finiteness, msc:03E25, msc:04A25, msc:26A03, msc:26A15, msc:54A35, msc:54D20

وصف الملف: application/pdf

Relation: mr:MR1485075; zbl:Zbl 0938.54008; reference:Bentley H.L., Herrlich H.: Countable choice and pseudometric spaces.in preparation. Zbl 0922.03068; reference:Herrlich H.: Compactness and the Axiom of Choice.Appl. Categ. Struct. 4 (1996), 1-14. Zbl 0881.54027, MR 1393958; reference:Herrlich H., Steprāns J.: Maximal Filters, continuity, and choice principles.to appear in Quaestiones Math. MR 1625478; reference:Jaegermann M.: The axiom of choice and two definitions of continuity.Bulletin de l'Acad. Polonaise des Sciences, Ser. Math. 13 (1965), 699-704. Zbl 0252.02059, MR 0195711; reference:Jech T.: Eine Bemerkung zum Auswahlaxiom.Časopis pro pěstování matematiky 9 (1968), 30-31. Zbl 0167.27402, MR 0233706; reference:Sierpiński W.: Sur le rôle de l'axiome de M. Zermelo dans l'Analyse moderne.Compt. Rendus Hebdomadaires des Séances de l'Academie des Sciences, Paris 193 (1916), 688-691.; reference:Sierpiński W.: L'axiome de M. Zermelo et son rôle dans la théorie des ensembles et l'analyse.Bulletin de l'Académie des Sciences de Cracovie, Classe des Sciences Math., Sér. A (1918), 97-152.

الاتاحة: http://hdl.handle.net/10338.dmlcz/118952

المؤلفون: Matijević, Vlasta

مصطلحات موضوعية: keyword:approximate inverse system, keyword:approximate inverse limit, keyword:approximate resolution $\operatorname{mod}\, \Cal P$, keyword:realcompact space, keyword:Lindelöf space, keyword:Polish space, keyword:non-measurable cardinal, msc:54B25, msc:54B35, msc:54C56, msc:54D30, msc:54D60

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/118805

المؤلفون: Arhangel'skii, A. V.

مصطلحات موضوعية: keyword:Lindelöf space, keyword:Souslin number, keyword:spread, keyword:extent, keyword:pseudocharacter, keyword:relative cardinal invariant, msc:54A25, msc:54D20

وصف الملف: application/pdf

Relation: mr:MR1357532; zbl:Zbl 0837.54005; reference:[1] Arhangel'skii A.V.: On the cardinality of bicompacta satisfying the first axiom of countability.Soviet Math. Dokl. 10 (1969), 951-955. MR 0119188; reference:[2] Arhangel'skii A.V.: Structure and classification of topological spaces and cardinal invariants.Russian Math. Surveys 33 (1978), 33-96. MR 0526012; reference:[3] Arhangel'skii A.V.: Theorems on the cardinality of families of sets in compact Hausdorff spaces.Soviet Math. Dokl. 17:1 (1976), 213-217. MR 0405327; reference:[4] Arhangel'skii A.V.: A theorem on cardinality.Russ. Math. Surveys 34:4 (1979), 153-154. MR 0548421; reference:[5] Arhangel'skii A.V., Hamdi M.M. Genedi: The beginnings of the Theory of Relative Topological Properties.p. 3-48 in: General Topology. Spaces and Functions, Izd. MGU, Moscow, 1989 (in Russian).; reference:[6] Arhangel'skii A.V.: $C_p$-Theory.in: M. Hušek and J. van Mill, Editors, Chapter 1, p. 1-56, North-Holland, Amsterdam, 1992. Zbl 0932.54015; reference:[7] Arhangel'skii V.A.: Relative compactness and networks.Master Thesis, Moscow State University, (1994), Preprint, p. 1-4, (in Russian).; reference:[8] Bell M., Ginsburg J., Woods G.: Cardinal inequalities for topological spaces involving the weak Lindelöf number.Pacific J. Math. 79 (1978), 37-45. MR 0526665; reference:[9] Burke D.K., Hodel R.E.: The number of compact subsets of a topological space.Proc. Amer. Math. Soc. 58 (1976), 363-368. Zbl 0335.54005, MR 0418014; reference:[10] Charlesworth A.: On the cardinality of a topological space.Proc. Amer. Math. Soc. 66 (1977), 138-142. Zbl 0364.54004, MR 0451184; reference:[11] Corson H.H., Michael E.: Metrization of certain countable unions.Illinois J. Math. 8 (1964), 351-360. MR 0170324; reference:[12] Dow A., Vermeer J.: An example concerning the property of a space being Lindelöf in another.Topology and Appl. 51 (1993), 255-260. Zbl 0827.54014, MR 1237391; reference:[13] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl 0684.54001, MR 1039321; reference:[14] Fedorchuk V.V.: On the cardinality of hereditarily separable compact Hausdorff spaces.Soviet Math. Dokl. 16 (1975), 651-655. Zbl 0331.54029; reference:[15] Ginsburg J., Woods G.: A cardinal inequality for topological spaces involving closed discrete sets.Proc. Amer. Math. Soc. 64 (1977), 357-360. Zbl 0398.54002, MR 0461407; reference:[16] Grothendieck A.: Criteres de compacticite dans les espaces fonctionnels genereaux.Amer. J. Math. 74 (1952), 168-186. MR 0047313; reference:[17] Gryzlow A.A.: Two theorems on the cardinality of topological spaces.Soviet Math. Dokl. 21 (1980), 506-509.; reference:[18] Hajnal A., Juhász I.: Discrete subspaces of topological spaces.Indag. Math. 29 (1967), 343-356. MR 0229195; reference:[19] Hodel R.E.: A technique for proving inequalities in cardinal functions.Topology Proc. 4 (1979), 115-120. MR 0583694; reference:[20] Hodel R.E.: Cardinal Functions, 1.in: Handbook of Set-theoretic Topology, Editors: Kunen K. and J.E. Vaughan, Chapter 1, 1-62, North-Holland, Amsterdam, 1984. MR 0776620; reference:[21] Hodel R.E.: Combinatorial set theory and cardinal function inequalities.Proc. Amer. Math. Soc. 111:2 (1991), 567-575. Zbl 0713.54007, MR 1039531; reference:[22] Mischenko A.: Spaces with point countable bases.Soviet Math. Dokl. 3 (1962), 855-858.; reference:[23] Pol R.: Short proofs of two theorems on cardinality of topological spaces.Bull. Acad. Polon. Sci. 22 (1974), 1245-1249. Zbl 0295.54004, MR 0383333; reference:[24] Ranchin D.V.: On compactness modulo an ideal.Dokl. AN SSSR 202 (1972), 761-764 (in Russian). MR 0296899; reference:[25] Shapirovskij B.E.: On discrete subspaces of topological spaces; weight, tightness and Souslin number.Soviet Math. Dokl. 13 (1972), 215-219.; reference:[26] Shapirovskij B.E.: Canonical sets and character. Density and weight in compact spaces.Soviet Math. Dokl. 15 (1974), 1282-1287. Zbl 0306.54012; reference:[27] Stephenson R.M., Jr.: Initially $\kappa $-compact and related spaces.in: Handbook of Set-theoretic Topology, Editors: Kunen K. and J.E. Vaughan, Chapter 13, 603-632, North-Holland, Amsterdam, 1984. Zbl 0588.54025, MR 0776632; reference:[28] van Douwen Eric K.: Applications of maximal topologies.Topol. and Appl. 51:2 (1993), 125-139. Zbl 0845.54028, MR 1229708

الاتاحة: http://hdl.handle.net/10338.dmlcz/118759

المؤلفون: Sakai, Masami

مصطلحات موضوعية: keyword:function space, keyword:pointwise convergence, keyword:linearly ordered topological space, keyword:Lindelöf space, keyword:Cantor tree, msc:54C25, msc:54C30, msc:54C35, msc:54D20

وصف الملف: application/pdf

Relation: mr:MR1173758; zbl:Zbl 0788.54019; reference:[1] Arkhangel'skii A.V.: Problems in $C_p$-theory.in: J. van Mill and G.M. Reed, Eds., {Open Problems in Topology}, North-Holland, 1990, 601-615. Zbl 0994.54020, MR 1078667; reference:[2] Engelking R.: General Topology.Sigma Series in Pure Math. 6, Helderman Verlag, Berlin, 1989. Zbl 0684.54001, MR 1039321; reference:[3] Lutzer D.J.: On generalized ordered spaces.Dissertationes Math. 89 (1971). Zbl 0228.54026, MR 0324668; reference:[4] Mill J. van: Supercompactness and Wallman spaces.Mathematical Centre Tracts 85 (1977). MR 0464160; reference:[5] Mill J. van, Mills C.F.: On the character of supercompact spaces.Top. Proceed. 3 (1978), 227-236. MR 0540493

الاتاحة: http://hdl.handle.net/10338.dmlcz/118482