| Title:
|
Continuous selections, $G_\delta $-subsets of Banach spaces and usco mappings (English) |
| Author:
|
Gutev, Valentin G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
533-538 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Every l.s.c\. mapping from a paracompact space into the non-empty, closed, convex subsets of a (not necessarily convex) $G_\delta $-subset of a Banach space admits a single-valued continuous selection provided every such mapping admits a convex-valued usco selection. This leads us to some new partial solutions of a problem raised by E. Michael. (English) |
| Keyword:
|
set-valued mapping |
| Keyword:
|
lower semi-continuous |
| Keyword:
|
upper semi-continuous |
| Keyword:
|
selection |
| Keyword:
|
countable-dimensional space |
| MSC:
|
46B20 |
| MSC:
|
46N10 |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 0840.54023 |
| idMR:
|
MR1307280 |
| . |
| Date available:
|
2009-01-08T18:13:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118693 |
| . |
| Reference:
|
[1] Gutev V.: Open mappings looking like projections.Set-valued Analysis 1 (1993), 247-260. Zbl 0818.54011, MR 1249265 |
| Reference:
|
[2] Michael E.: Continuous selections I.Ann. of Math. 63 (1956), 361-382. Zbl 0071.15902, MR 0077107 |
| Reference:
|
[3] Michael E.: Continuous selections II.Ann. of Math. 64 (1956), 562-580. Zbl 0073.17702, MR 0080909 |
| Reference:
|
[4] Michael E.: A theorem on semi-continuous set-valued functions.Duke Math. J. 26:4 (1959), 647-656. Zbl 0151.30805, MR 0109343 |
| Reference:
|
[5] Michael E.: Continuous selections avoiding a set.Top. Appl. 28 (1988), 195-213. Zbl 0654.54014, MR 0931523 |
| Reference:
|
[6] Michael E.: .in Open problems in Topology, J. van Mill and J.M. Reed, Chapter 17, 272-278, North-Holland, Amsterdam 1990. Zbl 1171.90455, MR 1078636 |
| Reference:
|
[7] Michael E.: Some refinements of a selection theorem with 0-dimensional domain.Fund. Math. 140 (1992), 279-287. Zbl 0763.54015, MR 1173768 |
| Reference:
|
[8] J. van Mill: Infinite Dimensional Topology.Prerequisites and Introduction, North-Holland, Amsterdam, 1989. Zbl 1027.57022, MR 0977744 |
| Reference:
|
[9] Nedev S.: Selection and factorization theorems for set-valued mappings.Serdica 6 (1980), 291-317. Zbl 0492.54006, MR 0644284 |
| . |
