| Title:
|
Closed embeddings into complements of $\Sigma$-products (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Hušek, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
647-655 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a $\Sigma$-subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and negation of CH, no countable nowhere dense space is a co-Valdivia space. (English) |
| Keyword:
|
$\Sigma$-product |
| Keyword:
|
Tikhonov cube |
| Keyword:
|
Valdivia compact |
| Keyword:
|
locally compact space |
| MSC:
|
54B10 |
| MSC:
|
54C25 |
| MSC:
|
54D35 |
| MSC:
|
54D45 |
| idZBL:
|
Zbl 1212.54082 |
| idMR:
|
MR2493944 |
| . |
| Date available:
|
2009-05-05T17:13:42Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119752 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: Two types of remainders of topological groups.Comment. Math. Univ. Carolin. 49 (2008), 119-126. Zbl 1212.54086, MR 2433629 |
| Reference:
|
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| Reference:
|
[3] Kalenda O.: Valdivia compact spaces in topology and Banach space theory.Extracta Math. 15 (2000), 1-85. Zbl 0983.46021, MR 1792980 |
| Reference:
|
[4] Kalenda O.: On the class of continuous images of Valdivia compacta.Extracta Math. 18 (2003), 65-80. Zbl 1159.46306, MR 1989298 |
| Reference:
|
[5] Noble N.: The continuity of functions on Cartesian products.Trans. Amer. Math. Soc. 149 (1970), 187-198. Zbl 0229.54028, MR 0257987, 10.1090/S0002-9947-1970-0257987-5 |
| Reference:
|
[6] Šapirovskii B.: On the density of topological spaces.Soviet Math. Dokl. 13 (1972), 1271-1275. MR 0383331 |
| Reference:
|
[7] Šapirovskii B.: On separability and metrizability of spaces with Souslin's condition.Soviet Math. Dokl. 13 (1972), 1633-1638. MR 0322801 |
| Reference:
|
[8] Tall F.D.: The countable chain condition versus separability - applications of Martin's axiom.General Topology Appl. 4 (1974), 315-339. Zbl 0293.54003, MR 0423284, 10.1016/0016-660X(74)90010-5 |
| . |
