| Title:
|
Choice principles in elementary topology and analysis (English) |
| Author:
|
Herrlich, Horst |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
545-552 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results --- old and new --- that specify how much ``choice'' is needed {\it precisely} to validate each of certain basic analytical and topological results. (English) |
| Keyword:
|
Axiom of (Countable) Choice |
| Keyword:
|
Boolean Prime Ideal Theorem |
| Keyword:
|
Theorems of Ascoli |
| Keyword:
|
Baire |
| Keyword:
|
Čech-Stone and Tychonoff |
| Keyword:
|
compact |
| Keyword:
|
Lindelöf and orderable spaces |
| MSC:
|
03E25 |
| MSC:
|
04A25 |
| MSC:
|
26A03 |
| MSC:
|
26A15 |
| MSC:
|
54A35 |
| MSC:
|
54B10 |
| MSC:
|
54C35 |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| MSC:
|
54D65 |
| MSC:
|
54E45 |
| MSC:
|
54E50 |
| MSC:
|
54E52 |
| idZBL:
|
Zbl 0938.54007 |
| idMR:
|
MR1485074 |
| . |
| Date available:
|
2009-01-08T18:36:05Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118951 |
| . |
| 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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| . |
