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.

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 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.