| Title:
|
On a question of E.A. Michael (English) |
| Author:
|
Filippov, Vladimir V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
735-737 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A negative answer to a question of E.A. Michael is given: A convex $G_\delta$-subset $Y$ of a Hilbert space is constructed together with a l.s.c. map $Y\to Y$ having closed convex values and no continuous selection. (English) |
| Keyword:
|
l.s.c. map |
| Keyword:
|
selection |
| Keyword:
|
space of probability measures |
| MSC:
|
54C65 |
| idZBL:
|
Zbl 1097.54024 |
| idMR:
|
MR2103087 |
| . |
| Date available:
|
2009-05-05T16:48:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119497 |
| . |
| Reference:
|
[1] Michael E.A.: Continuous selections, I.Ann. of Math. (1956), 63 361-382. Zbl 0071.15902, MR 0077107 |
| Reference:
|
[2] Michael E.A.: Some problems.in: Open Problems in Topology, J. van Mill, G.M. Reed, eds., North Holland, Amsterdam, 1990, pp.271-278. Zbl 1074.11018, MR 1078653 |
| Reference:
|
[3] Gutev V.G.: Continuous selections, $G_{\delta}$-subsets of Banach spaces and usco mappings.Comment. Math. Univ. Carolinae (1994), 35.3 533-538. MR 1307280 |
| Reference:
|
[4] Gutev V.G., Valov V.: Continuous selections and $C$-spaces.Proc. Amer. Math. Soc. (2002), 130 233-242. Zbl 0977.54017, MR 1855641 |
| Reference:
|
[5] Repovš D., Semenov P.V.: Continuous selections of multivalued mappings.in: Recent Progress in General Topology, M. Hušek, J. van Mill, eds., Elsevier Science B.V., 2002, pp.424-461. MR 1970007 |
| Reference:
|
[6] von Weizsäcker H.: A note on infinite dimensional convex sets.Math. Scand. (1976), 38 321-324. MR 0428009 |
| Reference:
|
[7] Hilton P.J., Wylie S.: Homology Theory.Cambridge University Press, New York, 1960. Zbl 0163.17803, MR 0115161 |
| . |
