On Semicompact Sets and Associated Properties

We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of su...

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Main Author: Mohammad S. Sarsak
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2009/465387
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author Mohammad S. Sarsak
author_facet Mohammad S. Sarsak
author_sort Mohammad S. Sarsak
collection DOAJ
description We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of such spaces, it is mainly shown that a semi-𝑇2 semicompact space is 𝑆𝐶𝑆 if and only if it is extremally disconnected. It is also shown that in an 𝑜𝑠-regular space 𝑋 if every point has an 𝑆𝐶𝑆 neighborhood, then 𝑋 is 𝑆𝐶𝑆.
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spelling doaj-art-01e1a2d5dc2b44fdaeef22c0f8d50d782025-08-20T02:01:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/465387465387On Semicompact Sets and Associated PropertiesMohammad S. Sarsak0Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 150459, Zarqa 13115, JordanWe continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆𝐶𝑆 spaces is given, where a space 𝑋 is 𝑆𝐶𝑆 if every subset of 𝑋 which is semicompact in 𝑋 is semiclosed; we study several properties of such spaces, it is mainly shown that a semi-𝑇2 semicompact space is 𝑆𝐶𝑆 if and only if it is extremally disconnected. It is also shown that in an 𝑜𝑠-regular space 𝑋 if every point has an 𝑆𝐶𝑆 neighborhood, then 𝑋 is 𝑆𝐶𝑆.http://dx.doi.org/10.1155/2009/465387
spellingShingle Mohammad S. Sarsak
On Semicompact Sets and Associated Properties
International Journal of Mathematics and Mathematical Sciences
title On Semicompact Sets and Associated Properties
title_full On Semicompact Sets and Associated Properties
title_fullStr On Semicompact Sets and Associated Properties
title_full_unstemmed On Semicompact Sets and Associated Properties
title_short On Semicompact Sets and Associated Properties
title_sort on semicompact sets and associated properties
url http://dx.doi.org/10.1155/2009/465387
work_keys_str_mv AT mohammadssarsak onsemicompactsetsandassociatedproperties