| Title:
|
On the cardinality of functionally Hausdorff spaces (English) |
| Author:
|
Fedeli, Alessandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
797-801 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: \noindent {\rm (i)} If $\,X$ is a functionally Hausdorff space then $|X| \leq 2^{fs(X) \psi_{\tau}(X)}$; \noindent {\rm (ii)} Let $X$ be a functionally Hausdorff space with $fs(X) \leq \kappa$. Then there is a subset $S$ of $X$ such that $|S| \leq 2^{\kappa}$ and $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$. (English) |
| Keyword:
|
cardinal functions |
| Keyword:
|
$\tau$-pseudocharacter |
| Keyword:
|
functional spread |
| MSC:
|
54A25 |
| MSC:
|
54D10 |
| MSC:
|
54D70 |
| idZBL:
|
Zbl 0886.54004 |
| idMR:
|
MR1440709 |
| . |
| Date available:
|
2009-01-08T18:27:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118886 |
| . |
| Reference:
|
[1] Engelking R.: General Topology. Revised and completed edition.Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). MR 1039321 |
| Reference:
|
[2] Fedeli A.: Two cardinal inequalities for functionally Hausdorff spaces.Comment. Math. Univ. Carolinae 35.2 (1994), 365-369. Zbl 0807.54006, MR 1286584 |
| Reference:
|
[3] Fedeli A., Watson S.: Elementary Submodels in Topology.submitted. |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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[10] Schröder J.: Urysohn cellularity and Urysohn spread.Math. Japonicae 38 (1993), 1129-1133. MR 1250339 |
| Reference:
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[11] Shapirovskii B.: On discrete subspaces of topological spaces. Weight, tightness and Suslin number.Soviet Math. Dokl. 13 (1972), 215-219. |
| Reference:
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[12] Sun S.H., Choo K.G.: Some new cardinal inequalities involving a cardinal function less than the spread and the density.Comment. Math. Univ. Carolinae 31.2 (1990), 395-401. Zbl 0717.54002, MR 1077911 |
| Reference:
|
[13] Watson S.: The construction of topological spaces: Planks and Resolutions.Recent Progress in General Topology, (Hušek M. and Van Mill J., eds.) Elsevier Science Publishers, B.V., North Holland, 1992, pp. 675-757. Zbl 0803.54001, MR 1229141 |
| Reference:
|
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| . |
