Continuous actions of pseudocompact groups and axioms of topological group

Abstract

summary:In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class $\mathcal N$ of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces $\mathcal N$ that gives some new examples and statements for the $C_p$-theory and theory of topologically homogeneous spaces.