| Title:
|
On a selection theorem of Blum and Swaminathan (English) |
| Author:
|
Yamauchi, Takamitsu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
681-691 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Blum and Swaminathan [Pacific J. Math. 93 (1981), 251--260] introduced the notion of $\Cal B$-fixedness for set-valued mappings, and characterized realcompactness by means of continuous selections for Tychonoff spaces of non-measurable cardinal. Using their method, we obtain another characterization of realcompactness, but without any cardinal assumption. We also characterize Dieudonné completeness and Lindelöf property in similar formulations. (English) |
| Keyword:
|
set-valued mapping |
| Keyword:
|
selection |
| Keyword:
|
realcompact |
| Keyword:
|
Dieudonné complete |
| Keyword:
|
Lindelöf |
| Keyword:
|
$\Cal B$-fixed |
| Keyword:
|
local intersection property |
| Keyword:
|
open lower sections |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| MSC:
|
54D20 |
| MSC:
|
54D60 |
| idZBL:
|
Zbl 1098.54017 |
| idMR:
|
MR2103083 |
| . |
| Date available:
|
2009-05-05T16:48:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119493 |
| . |
| Reference:
|
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| Reference:
|
[2] Blum I., Swaminathan S.: Continuous selections and realcompactness.Pacific J. Math. 93 (1981), 251-260. Zbl 0457.54012, MR 0623561 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[12] Wu X., Shen S.: A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications.J. Math. Anal. Appl. 197 (1996), 61-74. Zbl 0852.54019, MR 1371276 |
| Reference:
|
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| . |
