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International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 465387, 8 pages
Research Article

On Semicompact Sets and Associated Properties

Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan

Received 27 October 2009; Accepted 24 December 2009

Academic Editor: Naseer Shahzad

Copyright © 2009 Mohammad S. Sarsak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We continue the study of semicompact sets in a topological space. Several properties, mapping properties of semicompact sets are studied. A special interest to 𝑆 𝐢 𝑆 spaces is given, where a space 𝑋 is 𝑆 𝐢 𝑆 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- 𝑇 2 semicompact space is 𝑆 𝐢 𝑆 if and only if it is extremally disconnected. It is also shown that in an π‘œ 𝑠 -regular space 𝑋 if every point has an 𝑆 𝐢 𝑆 neighborhood, then 𝑋 is 𝑆 𝐢 𝑆 .