A note on spaces which have countable tightness
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In this paper, we introduce closure operators [·]_c and [·]_a on a space and study some relations among [·]_c, [·]_a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr(특수문자)chet-Urysohn property which is equivalent to countable tightness.
Abstract
In this paper, we introduce closure operators [·]_c and [·]_a on a space and study some relations among [·]_c, [·]_a and countable tightness. We introduce the concepts of a strongly sequentially closed set and a strongly sequentially open set and show that a space X has countable tightness if and only if every strongly sequentially closed set is closed if and only if every strongly sequentially open set is open. Finally we find a generalization of the weak Fr(특수문자)chet-Urysohn property which is equivalent to countable tightness.
참고문헌 (12)
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