| Title:
|
A semifilter approach to selection principles II: $\tau^\ast$-covers (English) |
| Author:
|
Zdomskyy, Lyubomyr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
539-547 |
| . |
| Category:
|
math |
| . |
| Summary:
|
\font\mathsf=csss10 at 8pt Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property $\bigcup_{\operatorname{fin}}(\Cal O, \operatorname{T}^\ast)$ provided $(\frak u<\frak g)$, and every space with the property $\bigcup_{\operatorname{fin}}(\Cal O, \operatorname{T}^\ast)$ is Hurewicz provided $(\operatorname{Depth}^+([\omega]^{\aleph_0})\leq \frak b)$. Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties $\text{\mathsf P}$ and $\text{\mathsf Q}$ [do not] coincide, where $\text{\mathsf P}$ and $\text{\mathsf Q}$ run over $\bigcup_{\operatorname{fin}}(\Cal O,\Gamma )$, $\bigcup_{\operatorname{fin}}(\Cal O, \operatorname{T})$, $\bigcup_{\operatorname{fin}}(\Cal O, \operatorname{T}^\ast)$, $\bigcup_{\operatorname{fin}}(\Cal O, \Omega )$, and $\bigcup_{\operatorname{fin}}(\Cal O, \Cal O)$. (English) |
| Keyword:
|
selection principle |
| Keyword:
|
semifilter |
| Keyword:
|
small cardinals |
| MSC:
|
03Axx |
| MSC:
|
03E17 |
| MSC:
|
03E35 |
| idZBL:
|
Zbl 1150.03016 |
| idMR:
|
MR2281015 |
| . |
| Date available:
|
2009-05-05T16:59:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119614 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/119546 |
| . |
| Reference:
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| . |
