| Title:
|
$\Sigma$-products and selections of set-valued mappings (English) |
| Author:
|
Shishkov, Ivailo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
203-207 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Every lower semi-continuous closed-and-convex valued mapping $\Phi : X\rightarrow 2^{Y}$, where $X$ is a $\Sigma$-product of metrizable spaces and $Y$ is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author. (English) |
| Keyword:
|
set-valued mapping |
| Keyword:
|
l.s.c. mapping |
| Keyword:
|
$\Sigma$-product |
| Keyword:
|
selection |
| MSC:
|
54B10 |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| MSC:
|
54D15 |
| idZBL:
|
Zbl 1053.54029 |
| idMR:
|
MR1825384 |
| . |
| Date available:
|
2009-01-08T19:09:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119235 |
| . |
| Reference:
|
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| Reference:
|
[2] Choban M., Nedev S.: Continuous selections for mappings with generalized ordered domain.Math. Balkanica, New Series 11 , Fasc. 1-2 (1997), 87-95. Zbl 0943.46003, MR 1606612 |
| Reference:
|
[3] Corson H.: Normality of subsets of product spaces.Amer. J. Math. 81 (1959), 785-796. MR 0107222 |
| Reference:
|
[4] Dieudonné J.: Une généralisation des espaces compacts.J. de Math. Pures et Appl. 23 (1944), 65-76. MR 0013297 |
| Reference:
|
[5] Engelking R.: General Topology.PWN, Warszawa, 1985. Zbl 0684.54001 |
| Reference:
|
[6] Gul'ko S.P.: Properties of sets lying in $\Sigma$-products.Dokl. AN SSSR, 1977. |
| Reference:
|
[7] Ishii T.: Paracompactness of topological completions.Fund. Math. 92 (1976), 65-77. Zbl 0354.54009, MR 0418039 |
| Reference:
|
[8] Katětov M.: On the extension of locally finite coverings (in Russian).Colloq. Math. 6 (1958), 145-151. MR 0103450 |
| Reference:
|
[9] Michael E.: Continuous selections: I.Ann. Math. 63 (1956), 562-590. Zbl 0071.15902, MR 0077107 |
| Reference:
|
[10] Rudin M.E.: $\Sigma$-products of metric spaces are normal.preprint (see [5], the problems to Chapter 4). |
| Reference:
|
[11] Shishkov I.: Extensions of l.s.c. mappings into reflexive Banach spaces.Set-Valued Analysis, to appear. Zbl 1018.54012, MR 1888457 |
| Reference:
|
[12] Shishkov I.: Selections of l.s.c. mappings into Hilbert spaces.Compt. rend. Acad. Bulg. Sci. 53.7 (2000). MR 1779519 |
| . |
