| Title:
|
Nowhere dense subsets and Booth's Lemma (English) |
| Author:
|
Malykhin, V. I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
391-395 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The following statement is proved to be independent from $[\operatorname{LB}+\neg \operatorname{CH}]$: \linebreak $(*)$ Let $X$ be a Tychonoff space with $c(X)\leq \aleph _0$ and $\pi w(X)<\frak C$. Then a union of less than $\frak C$ of nowhere dense subsets of $X$ is a union of not greater than $\pi w(X)$ of nowhere dense subsets. (English) |
| Keyword:
|
nowhere dense subset |
| Keyword:
|
Booth's Lemma |
| Keyword:
|
$\pi $-weight |
| MSC:
|
03E35 |
| MSC:
|
03E50 |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| idZBL:
|
Zbl 0854.54005 |
| idMR:
|
MR1399011 |
| . |
| Date available:
|
2009-01-08T18:24:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118841 |
| . |
| Reference:
|
[1] Rudin M.E.: Martin's Axiom.in Handbook of set-theoretic topology K. Kunen and J.E. Vaughan Elsevier Science Publishers B.V. (1984), 491-501. |
| Reference:
|
[2] Bell M.G.: On the combinatorial Principle $P({\frak C})$.Fund. Math. 114 (1981), 149-157. Zbl 0581.03038, MR 0643555 |
| . |
