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

- Journal title : Communications of the Korean Mathematical Society
- Volume 25, Issue 3, 2010, pp.477-484
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2010.25.3.477

Title & Authors

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

Hong, Woo-Chorl;

Hong, Woo-Chorl;

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 (*).

Keywords

Frchet-Urysohn;sequential;AP;WAP;countable tightness;weakly discretely generated;compact;countably compact;sequentially compact and property(*);

Language

English

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