| Title:
|
An answer to a question of Arhangel'skii (English) |
| Author:
|
Michalewski, Henryk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
545-550 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that there exists an example of a metrizable non-discrete space $X$, such that $C_p(X\times \omega )\approx_{l} C_p(X)$ but $C_p(X\times S) \not\approx_{l} C_p(X)$ where $S = (\{0\}\cup\{\frac{1}{n+1}:n\in\omega \})$ and $C_p(X)$ is the space of all continuous functions from $X$ into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel'skii ([2, Problem 4]). (English) |
| Keyword:
|
topology of pointwise convergence |
| MSC:
|
46E10 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 1053.54025 |
| idMR:
|
MR1860243 |
| . |
| Date available:
|
2009-01-08T19:16:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119269 |
| . |
| 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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| . |
