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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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