| Title:
|
Mesocompactness and selection theory (English) |
| Author:
|
Yan, Peng-fei |
| Author:
|
Yang, Zhongqiang |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
149-157 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A topological space $X$ is called mesocompact (sequentially mesocompact) if for every open cover ${\mathcal U}$ of $X$, there exists an open refinement ${\mathcal V}$ of ${\mathcal U}$ such that $\{V\in {\mathcal V}: V\cap K\neq \emptyset\}$ is finite for every compact set (converging sequence including its limit point) $K$ in $X$. In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory. (English) |
| Keyword:
|
selections |
| Keyword:
|
l.s.c. set-valued maps |
| Keyword:
|
mesocompact |
| Keyword:
|
sequentially mesocompact |
| Keyword:
|
persevering compact set-valued maps |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| idZBL:
|
Zbl 1249.54046 |
| idMR:
|
MR2880917 |
| . |
| Date available:
|
2012-02-07T10:29:56Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141832 |
| . |
| Reference:
|
[1] Boone J.R.: Some characterization of paracompactness in $\chi $-space.Fund. Math. 72 (1971), 145–155. MR 0295291 |
| Reference:
|
[2] Choban M.: Many-valued mappings and Borel sets, II.Trans. Moscow Math. Soc. 23 (1970), 286–310. |
| Reference:
|
[3] Engelking R.: General Topology.Revised and completed edition, Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[4] Michael E.: A theorem on semicontinuous set-valued funtions.Duke Math. 26 (1956), 647–652. MR 0109343, 10.1215/S0012-7094-59-02662-6 |
| Reference:
|
[5] Michael E.: Topologies on spaces of subsets.Trans. Amer. Math. Soc. 71 (1951), 152–182. Zbl 0043.37902, MR 0042109, 10.1090/S0002-9947-1951-0042109-4 |
| Reference:
|
[6] Miyazaki K.: Characterizations of paracompact-like properties by means of set-valued semi-continuous selections.Proc. Amer. Math. Soc. 129 (2001), 2777–2782. Zbl 0973.54009, MR 1838802, 10.1090/S0002-9939-01-06204-9 |
| Reference:
|
[7] Nedev S.: Selection and factorization theorems for set-valued mapings.Serdica 6 (1980), 291–317. MR 0644284 |
| Reference:
|
[8] Yan P.-F.: $\tau$ selections and its applictions on BCO.J. Math. (in Chinese) 17 (1997), 547–551. MR 1675535 |
| . |
