9 THE CONTINUITY OF THE INVERSION AND THE STRUCTURE OF MAXIMAL SUBGROUPS IN COUNTABLY COMPACT TOPOLOGICAL SEMIGROUPS
2015
In this paper all topological spaces will be assumed to be Hausdorff. We shall follow the terminology of [1, 2, 3]. A topological space X is called countably compact if any countable open cover of X contains a finite subcover [3]. A topological space X is called pseudocompact if each continuous real-valued function on X is bounded [3]. A topological space X is called sequential if each non-closed subset A of X contains a sequence of points {xn}∞n=1 that converges to some point x ∈ X \\ A. A topological space X is called sequentially compact if each sequence {xn}∞n=1 ⊂ X has a convergent subsequence [3]. A semigroup is a set with a binary associative operation. An element e of a semigroup S is called an idempotent if ee = e. If S is a semigroup, then by E(S) we denote the subset of all idempotents of S. For a semigroup S let