| Title:
|
On a question of $C_c(X)$ (English) |
| Author:
|
Olfati, A. R. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
253-260 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of $C(X)$, Rend. Sem. Mat. Univ. Padova 129 (2013), 47--69. It is shown that $C_c(X)$ is isomorphic to some ring of continuous functions if and only if $\upsilon_0 X$ is functionally countable. For a strongly zero-dimensional space $X$, this is equivalent to say that $X$ is functionally countable. Hence for every $P$-space it is equivalent to pseudo-$\aleph_0$-compactness. (English) |
| Keyword:
|
zero-dimensional space |
| Keyword:
|
strongly zero-dimensional space |
| Keyword:
|
$\mathbb{N}$-compact space |
| Keyword:
|
Banaschewski compactification |
| Keyword:
|
character |
| Keyword:
|
ring homomorphism |
| Keyword:
|
functionally countable subring |
| Keyword:
|
functional separability |
| MSC:
|
46E25 |
| MSC:
|
54C30 |
| MSC:
|
54C40 |
| MSC:
|
54D35 |
| MSC:
|
54D60 |
| idZBL:
|
Zbl 06604505 |
| idMR:
|
MR3513448 |
| DOI:
|
10.14712/1213-7243.2015.161 |
| . |
| Date available:
|
2016-07-05T15:12:45Z |
| Last updated:
|
2018-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145752 |
| . |
| Reference:
|
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