Academic Journal
A nice subclass of functionally countable spaces
| العنوان: | A nice subclass of functionally countable spaces |
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| المؤلفون: | Tkachuk, Vladimir V. |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 2018 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| 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 |
| الوصف: | summary:A space $X$ is {functionally countable} if $f(X)$ is countable for any continuous function $f\colon X \to {\mathbb{R}}$. We will call a space $X$ {exponentially separable} if for any countable family ${\mathcal{F}}$ of closed subsets of $X$, there exists a countable set $A\subset X$ such that $A\cap \bigcap {\mathcal{G}}\neq\emptyset$ whenever ${\mathcal{G}}\subset {\mathcal{F}}$ and $\bigcap {\mathcal{G}}\neq\emptyset$. Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has nice categorical properties: it is preserved by closed subspaces, countable unions and continuous images. Besides, it contains all Lindelöf $P$-spaces as well as some wide classes of scattered spaces. In particular, if a scattered space is either Lindelöf or ${\omega}$-bounded, then it is exponentially separable. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
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| الاتاحة: | http://hdl.handle.net/10338.dmlcz/147407 |
| 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.D329EF16 |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
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