On Semicompact Sets and Associated Properties

Mohammad S. Sarsak

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-8

Abstract:

We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𠑆 ð ¶ ð ‘† spaces is given, where a space ð ‘‹ is 𠑆 ð ¶ ð ‘† if every subset of ð ‘‹ which is semicompact in ð ‘‹ is semiclosed; we study several properties of such spaces, it is mainly shown that a semi- 𠑇 2 semicompact space is 𠑆 ð ¶ ð ‘† if and only if it is extremally disconnected. It is also shown that in an ð ‘œ ð ‘ -regular space ð ‘‹ if every point has an 𠑆 ð ¶ ð ‘† neighborhood, then ð ‘‹ is 𠑆 ð ¶ ð ‘† .

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:465387

DOI: 10.1155/2009/465387

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