| Title:
|
Disasters in metric topology without choice (English) |
| Author:
|
Tachtsis, Eleftherios |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
165-174 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that it is consistent with ZF that there is a dense-in-itself compact metric space $(X,d)$ which has the countable chain condition (ccc), but $X$ is neither separable nor second countable. It is also shown that $X$ has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply {\it the disjoint union of metrizable spaces is normal\/}. (English) |
| Keyword:
|
Axiom of Choice |
| Keyword:
|
Axiom of Multiple Choice |
| Keyword:
|
Principle of Dependent Choice |
| Keyword:
|
Ordering Principle |
| Keyword:
|
metric spaces |
| Keyword:
|
separable metric spaces |
| Keyword:
|
second countable metric spaces |
| Keyword:
|
paracompact spaces |
| Keyword:
|
compact T$_2$ spaces |
| Keyword:
|
ccc spaces. |
| MSC:
|
03E25 |
| MSC:
|
54A35 |
| MSC:
|
54D20 |
| MSC:
|
54E35 |
| MSC:
|
54E45 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1072.03030 |
| idMR:
|
MR1903316 |
| . |
| Date available:
|
2009-01-08T19:20:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119309 |
| . |
| 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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| Reference:
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| Reference:
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| . |
