| Title:
|
Condensations of Cartesian products (English) |
| Author:
|
Pavlov, Oleg |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
355-365 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space $X$ there is a $\mu$ such that $X^\mu$ can be condensed onto a normal ($\sigma$-compact) space if and only if there is no measurable cardinal. For any Tychonoff space $X$ and any cardinal $\nu$ there is a Tychonoff space $M$ which preserves many properties of $X$ and such that any one-to-one continuous image of $M^\mu$, $\mu\leq\nu$, contains a closed copy of $X^\mu$. For any infinite compact space $K$ there is a normal space $X$ such that $X\times K$ cannot be mapped one-to-one onto a normal space. (English) |
| Keyword:
|
condensation |
| Keyword:
|
one-to-one |
| Keyword:
|
compact |
| Keyword:
|
measurable |
| MSC:
|
54A10 |
| MSC:
|
54B10 |
| MSC:
|
54C10 |
| idZBL:
|
Zbl 0976.54008 |
| idMR:
|
MR1732657 |
| . |
| Date available:
|
2009-01-08T18:53:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119092 |
| . |
| 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:
|
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| . |
