Injectivity, projectivity, and the axiom of choice
نویسندگان
چکیده
منابع مشابه
The Axiom of Choice
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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Luce’s choice axiom (LCA) is a theory of individual choice behavior that has proven to be a powerful tool in the behavioral sciences for over 50 years. LCA is grounded in two fundamental properties: choice is probabilistic and the probability of choosing an option from one set of alternatives is related to the probability of choosing the same option from a different set. This entry reviews the ...
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We shall start with some definitions from topology. First of all, a metric space is a topological space whose topology is determined by a metric. A metric on a topological space X is a function d from X × X to R , the reals, which has the following properties: For all x, y, z ∈ X , (a) d(x, y) ≥ 0, (b) d(x, x) = 0, (c) if d(x, y) = 0, then x = y, (d) d(x, y) = d(y, x), and (e) d(x, y) + d(y, z)...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1979
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1979-0542870-6