Viglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is anH-set in the sense of Velǐcko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S-set in the sense of Dickman and Krystock. Such spaces are calledC-s-compact. Recently, the notion of strongly subclosed relation, introduced by Jose...

Answering recent question of A.V. Arhangel’skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

We introduce the class of linearly S-closed spaces as a proper subclass H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called if only any semi-open chain cover posses member dense in space. It shown that extremally disconnected coincide. gave characterizations these terms s-accumulation points filter bases complete families open subsets. While re...

By Isbell duality, each compact regular frame L is isomorphic to the frame of opens of a compact Hausdorff space X. In this note we study the spectrum Spec(L) of prime filters of a compact regular frame L. We prove that X is realized as the minimum of Spec(L) and the Gleason cover of X as the maximum of Spec(L). We also characterize zero-dimensional, extremally disconnected, and scattered compa...

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y . The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if each continuous function from a space X to Y is rc-continuous. The second concept studied is the...

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 extrema...