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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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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1988
ISSN: 0166-8641
DOI: 10.1016/0166-8641(88)90071-5