Sequential compactness and the axiom of choice.
نویسندگان
چکیده
منابع مشابه
Definitions of Compactness and The Axiom of Choice
We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.
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We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
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We propose that failures of the axiom of choice, that is, surjective functions admitting no sections, can be reasonably classified by means of invariants borrowed from algebraic topology. We show that cohomology, when defined so that its usual exactness properties hold even in the absence of the axiom of choice, is adequate for detecting failures of this axiom in the following sense. If a set X...
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Omar De la Cruz∗1, Eric J. Hall∗∗2, Paul Howard∗∗∗3, Kyriakos Keremedis†4, and Jean E. Rubin 1 Department of Statistics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA 2 Department of Mathematics and Statistics, University of Missouri, Kansas City, MO 64110, USA 3 Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA 4 Department of Mathemati...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1983
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093870222