| Title:
|
Baire-one mappings contained in a usco map (English) |
| Author:
|
Kalenda, Ondřej F. K. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
135-145 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in $\Bbb R^d$ is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map. (English) |
| Keyword:
|
Baire-one function |
| Keyword:
|
usco map |
| Keyword:
|
usco-bounded sequence of continuous functions |
| MSC:
|
26A21 |
| MSC:
|
54C60 |
| MSC:
|
54E45 |
| idZBL:
|
Zbl 1199.54121 |
| idMR:
|
MR2338835 |
| . |
| Date available:
|
2009-05-05T17:01:49Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119644 |
| . |
| Reference:
|
[1] Anguelov R., Kalenda O.: The convergence space of minimal usco mappings.preprint MATH-KMA-2006/197. MR 2486619 |
| Reference:
|
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| Reference:
|
[3] Hansell R.W.: First class functions with values in nonseparable spaces.Constantin Carathéodory: an international tribute, Vol. I, II, World Sci. Publishing, Teaneck, NJ, 1991, pp.461-475. Zbl 0767.54010, MR 1130849 |
| Reference:
|
[4] Hansell R.W., Jayne J.E., Talagrand M.: First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces.J. Reine Angew. Math. 361 (1985), 201-220. Zbl 0573.54012, MR 0807260 |
| Reference:
|
[5] Jayne J.E., Rogers C.A.: Borel selectors for upper semi-continuous set-valued mappings.Acta Math. 155 (1985), 41-79. MR 0793237 |
| Reference:
|
[6] Jayne J.E., Rogers C.A.: Selectors.Princeton University Press, Princeton, 2002. Zbl 1002.54001, MR 1915965 |
| Reference:
|
[7] Srivatsa V.V.: Baire class 1 selectors for upper semicontinuous set-valued maps.Trans. Amer. Math. Soc. 337 (1993), 2 609-624. Zbl 0822.54017, MR 1140919 |
| . |
