| Title:
|
On analyticity in cosmic spaces (English) |
| Author:
|
Okunev, Oleg |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
185-190 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a $K$-analytic space under a measurable mapping. We also obtain characterizations of analyticity and $\sigma $-compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if $X$ is a separable metrizable space and $Y$ is its dense subspace then the space of restricted continuous functions $C_p(X\mid Y)$ is analytic iff it is a $K_{\sigma \delta }$-space iff $X$ is $\sigma $-compact. (English) |
| Keyword:
|
measurable mapping |
| Keyword:
|
cosmic space |
| Keyword:
|
analyticity |
| Keyword:
|
topology of pointwise convergence |
| MSC:
|
54C35 |
| MSC:
|
54C50 |
| MSC:
|
54E20 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 0837.54009 |
| idMR:
|
MR1240216 |
| . |
| Date available:
|
2009-01-08T18:02:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118568 |
| . |
| 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:
|
[8] Okunev O.: On analyticity in non-metrizable spaces.Abstracts of the VII Prague Topol. Symp., p. 101. |
| Reference:
|
[9] Rogers C.A., Jayne J.E., and al.: Analytic Sets.Academic Press, London, 1980. |
| Reference:
|
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| . |
