International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 465387, 8 pages
doi:10.1155/2009/465387

On semicompact sets and associated properties

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.