Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT

  • Hong, Woo-Chorl (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
  • Received : 2008.01.09
  • Published : 2010.07.31
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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 (*).

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References

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