| Title:
|
On function spaces of Corson-compact spaces (English) |
| Author:
|
Bandlow, Ingo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
347-356 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We apply elementary substructures to characterize the space $C_p(X)$ for Corson-compact spaces. As a result, we prove that a compact space $X$ is Corson-compact, if $C_p(X)$ can be represented as a continuous image of a closed subspace of $(L_{\tau })^{\omega }\times Z$, where $Z$ is compact and $L_{\tau }$ denotes the canonical Lindelöf space of cardinality $\tau $ with one non-isolated point. This answers a question of Archangelskij [2]. (English) |
| Keyword:
|
function spaces |
| Keyword:
|
Corson-compact spaces |
| Keyword:
|
elementary substructures |
| MSC:
|
54C35 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 0835.54016 |
| idMR:
|
MR1286581 |
| . |
| Date available:
|
2009-01-08T18:11:30Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118673 |
| . |
| Reference:
|
[1] Amir D., Lindenstrauß J.: The structure of weakly compact sets in Banach spaces.Ann. Math. Ser. 2 88:1 (1968). MR 0228983 |
| Reference:
|
[2] Archangelskij A.V.: Topologicheskie prostranstva funkcij (in Russian).Moscow, 1989. |
| Reference:
|
[3] Bandlow I.: A construction in set theoretic topology by means of elementary substructures.Zeitschr. f. Math. Logik und Grundlagen d. Math. 37 (1991). Zbl 0769.54013, MR 1270189 |
| Reference:
|
[4] Bandlow I.: A characterization of Corson-compact spaces.Comment. Math. Univ. Carolinae 32 (1991). Zbl 0769.54025, MR 1159800 |
| Reference:
|
[5] Dow A.: An introduction to applications of elementary submodels to topology.Topology Proceedings, vol. 13, no. 1, 1988. Zbl 0696.03024, MR 1031969 |
| Reference:
|
[6] Engelking R.: General Topology.Warsaw, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[7] Kunen K.: Set Theory.Studies in Logic 102, North Holland, 1980. Zbl 0960.03033, MR 0597342 |
| Reference:
|
[8] Negrepontis S.: Banach spaces and topology.Handbook of set-theoretic topology, North Holland, 1984, 1045-1042. Zbl 0832.46005, MR 0776642 |
| Reference:
|
[9] Pol R.: On pointwise and weak topology in function spaces.Preprint Nr 4/84, Warsaw, 1984. |
| . |
