| Title:
|
Initially $\kappa$-compact spaces for large $\kappa$ (English) |
| Author:
|
Christodoulou, Stavros |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
319-325 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work presents some cardinal inequalities in which appears the closed pseu\-do-\-cha\-racter, $\psi_c$, of a space. Using one of them --- $\psi_c(X) \le 2^{d(X)}$ for $T_2$ spaces --- we improve, from $T_3$ to $T_2$ spaces, the well-known result that initially $\kappa$-compact $T_3$ spaces are $\lambda $-bounded for all cardinals $\lambda $ such that $2^\lambda \leq \kappa $. And then, using an idea of A. Dow, we prove that initially $\kappa $-compact $T_2$ spaces are in fact compact for $\kappa = 2^{F(X)}$, $2^{s(X)}$, $2^{t(X)}$, $2^{\chi (X)}$, $2^{\psi_c(X)}$ or $\kappa = \max\{\tau^+, \tau^{<\tau}\}$, where $\tau > t(p,X)$ for all $p \in X$. (English) |
| Keyword:
|
initially $\kappa $-compact space |
| Keyword:
|
$\kappa$-bounded space |
| Keyword:
|
closed pseudocharacter |
| Keyword:
|
cardinal inequalities |
| MSC:
|
54A25 |
| MSC:
|
54D10 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 0976.54022 |
| idMR:
|
MR1732652 |
| . |
| Date available:
|
2009-01-08T18:52:28Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119087 |
| . |
| Reference:
|
[BDFN] Balogh Z., Dow A., Fremlin D.H., Nyikos P.J.: Countable tightness and proper forcing.Bull. Amer. Math. Soc. 19 (1988), 295-298. Zbl 0661.54007, MR 0940491 |
| Reference:
|
[Chr] Christodoulou S.: Some topologies over a cardinal.Questions Answers Gen. Topology 10 (1992), 143-148. Zbl 0782.54002, MR 1180472 |
| Reference:
|
[D85] Dow A.: On initially $\kappa$-compact spaces.in Rings of Continuous Functions; C. Aull ed., Lecture Notes in Pure and Applied Math. 95, 1985, pp.103-108. MR 0789264 |
| Reference:
|
[D89] Dow A.: Compact spaces of countable tightness in the Cohen model.in Set Theory and Its Applications; LNM, 1401, 1989, pp.55-67. Zbl 0684.54003, MR 1031765 |
| Reference:
|
[Ho] Hodel R.: Cardinal functions I.in Handbook of Set-Theoretic Topology; K. Kunen and J.E. Vaughan eds., North-Holland, Amsterdam, 1984, pp.1-61. Zbl 0559.54003, MR 0776620 |
| Reference:
|
[Ju80] Juhasz J.: Cardinal functions in topology - ten years later.Mathematical Centre Tracts 123, Mathematical Centrum - Amsterdam, 1980. Zbl 0479.54001, MR 0576927 |
| Reference:
|
[Ju84] Juhasz J.: Cardinal functions II.in Handbook of Set-Theoretic Topology; K. Kunen and J.E. Vaughan eds., North-Holland, Amsterdam, 1984, pp.63-109. Zbl 0559.54004, MR 0776621 |
| Reference:
|
[Koz] Koszmider P.: Splitting ultrafilters of the thin-very tall algebra and initially $ømega_1$- compactness.preprint. |
| Reference:
|
[St] Stephenson R.M., Jr.: Initially $\kappa$-compact and related spaces.in Handbook Set-Theoretic Topology; K. Kunen and J.E. Vaughan eds., North-Holland, Amsterdam, 1984, pp. 603-632. Zbl 0588.54025, MR 0776632 |
| . |
