The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

Abstract

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\mathrm{inv}:H(S)\to H(S)$ is continuous; and (iv) the projection $\pi :H(S)\to E(S)$, $\pi :x⟼x{x}^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous.

References in corpus (1)

• On countably compact 0-simple topological inverse semigroups