| Title:
|
A note on condensations of $C_p(X)$ onto compacta (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Pavlov, O. I. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
485-492 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A condensation is a one-to-one continuous mapping onto. It is shown that the space $C_p(X)$ of real-valued continuous functions on $X$ in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum $X$ (Theorem 19). However, there exists a non-metrizable compactum $X$ such that $C_p(X)$ condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated. (English) |
| Keyword:
|
condensation |
| Keyword:
|
compactum |
| Keyword:
|
network |
| Keyword:
|
Lindelöf space |
| Keyword:
|
topology of pointwise convergence |
| Keyword:
|
$\sigma $-compact space |
| Keyword:
|
Eberlein compactum |
| Keyword:
|
Corson compactum |
| Keyword:
|
Borel set |
| Keyword:
|
monolithic space |
| Keyword:
|
tightness |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54C35 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1090.54003 |
| idMR:
|
MR1920523 |
| . |
| Date available:
|
2009-01-08T19:24:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119337 |
| . |
| 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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| . |
