| Title:
|
On a weak form of uniform convergence (English) |
| Author:
|
Fuka, Jaroslav |
| Author:
|
Holický, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
637-643 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of $\Delta $-convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Kat\v{e}tov around 1970 by showing that the only analytic metric spaces $X$ for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on $X$ implies $\Delta $-convergence are $\sigma$-compact spaces. We show that the assumption of analyticity cannot be omitted. (English) |
| Keyword:
|
continuous functions on metric spaces |
| Keyword:
|
pointwise convergence |
| Keyword:
|
$\Delta $-convergence |
| Keyword:
|
analytic spaces |
| Keyword:
|
Hurewicz theorem |
| Keyword:
|
$K_\sigma $-spaces |
| MSC:
|
40A30 |
| MSC:
|
54E35 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 1121.54058 |
| idMR:
|
MR2259495 |
| . |
| Date available:
|
2009-05-05T16:53:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119555 |
| . |
| 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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| . |
