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ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT

홍우철
대한수학회 (The Korean Mathematical Society)|2010.07|대한수학회논문집 (Communications of the KMS)|제25권 제3호|pp. 477-484

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참고문헌

키워드

WAPAPsequentialcountable tightnesscompactcountably compactFr´echet-Urysohnweakly discretely generatedsequentially compact and property (*).
주제분류수학

초록

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1)and (2), then compactness, countable compactness and sequential compactness are equivalent in X;(1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

Abstract

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1)and (2), then compactness, countable compactness and sequential compactness are equivalent in X;(1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

참고문헌 (18)

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