Academic Journal
A generic theorem in the theory of cardinal invariants of topological spaces
| العنوان: | A generic theorem in the theory of cardinal invariants of topological spaces |
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| المؤلفون: | Arhangel'skii, A. V. |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 1995 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:Lindelöf space, keyword:Souslin number, keyword:spread, keyword:extent, keyword:pseudocharacter, keyword:relative cardinal invariant, msc:54A25, msc:54D20 |
| الوصف: | summary:Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
| 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 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.DB23172B |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
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