On Semicompact Sets and Associated Properties

الملخص EN

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.