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On Semicompact Sets and Associated Properties

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  • Mohammad S. Sarsak

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 ‘† .

Suggested Citation

  • Mohammad S. Sarsak, 2009. "On Semicompact Sets and Associated Properties," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-8, February.
    • Handle: RePEc:hin:jijmms:465387
    DOI: 10.1155/2009/465387
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