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2011•Journal of Neijiang Normal UniversityRequires access

Notes on Baire Space and Meager Set

Wang Li

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Abstract

Certain properties of Baire space and Meager set and their connections are put under examination,and the proposition that any topological space X can be decomposed into two complementary sets such that one is of open(closed) Baire space and the other is of Meager set is also proved,and another equivalent form of Banach category theorem is also given and proved.

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What this paper is about

Certain properties of Baire space and Meager set and their connections are put under examination,and the proposition that any topological space X can be decomposed into two complementary sets such that one is of open(closed) Baire space and the other is of Meager set is also proved,and another equivalent form of Banach category theorem is also given and proved.

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Available abstract

Certain properties of Baire space and Meager set and their connections are put under examination,and the proposition that any topological space X can be decomposed into two complementary sets such that one is of open(closed) Baire space and the other is of Meager set is also proved,and another equivalent form of Banach category theorem is also given and proved.

Key concepts: Baire category theorem, Baire space, Baire measure, Mathematics, Complete metric space, Space (punctuation), Set (abstract data type), Banach space

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