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On semicompact sets and associated properties. (English) Zbl 1186.54023
Summary: We continue the study of semicompact sets in a topological space. Several properties, i.e. 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-$$T_{2}$$ 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 $$SCS$$.

##### MSC:
 54D30 Compactness
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##### References:
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