| Title:
|
Functional separability (English) |
| Author:
|
Levy, R. |
| Author:
|
Matveev, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
705-711 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $X$ is functionally countable (FC) if for every continuous $f:X\to \mathbb R$, $|f(X)|\leq \omega$. The class of FC spaces includes ordinals, some trees, compact scattered spaces, Lindelöf P-spaces, $\sigma$-products in $2^\kappa$, and some L-spaces. We consider the following three versions of functional separability: $X$ is 1-FS if it has a dense FC subspace; $X$ is 2-FS if there is a dense subspace $Y\subset X$ such that for every continuous $f:X\to \mathbb R$, $|f(Y)|\leq\omega$; $X$ is 3-FS if for every continuous $f:X\to \mathbb R$, there is a dense subspace $Y\subset X$ such that $|f(Y)|\leq \omega$. We give examples distinguishing 1-FS, 2-FS, and 3-FS and discuss some properties of functionally separable spaces. (English) |
| Keyword:
|
functionally countable |
| Keyword:
|
pseudo-$\aleph_1$-compact |
| Keyword:
|
DCCC |
| Keyword:
|
P-space |
| Keyword:
|
$\tau$-simple |
| Keyword:
|
scattered |
| Keyword:
|
1-functionally separable |
| Keyword:
|
2-functionally separable |
| Keyword:
|
3-functionally separable |
| Keyword:
|
pseudocompact |
| Keyword:
|
dyadic compactum |
| Keyword:
|
$\sigma$-centered base |
| Keyword:
|
LOTS |
| MSC:
|
54C30 |
| MSC:
|
54D65 |
| idZBL:
|
Zbl 1224.54063 |
| idMR:
|
MR2858271 |
| . |
| Date available:
|
2010-11-30T16:32:35Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140848 |
| . |
| Reference:
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