منابع مشابه
On the Baire Category Theorem
Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...
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In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (1) The axiom of dependent choice. (2) Products of compact Hausdorff spaces are Baire. (3) Products of pseudocompact spaces are Baire. (4) Products of countably compact, regular spaces are Baire. (5) Products of regular-closed spaces are Baire. (6) Products of Čech-complete...
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We study the uniform computational content of different versions of the Baire Category Theorem in the Weihrauch lattice. The Baire Category Theorem can be seen as a pigeonhole principle that states that a complete (i.e., “large”) metric space cannot be decomposed into countably many nowhere dense (i.e., “small”) pieces. The Baire Category Theorem is an illuminating example of a theorem that can...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2000
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00132-7