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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:
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