ANY SEMITOPOLOGICAL GROUP THAT IS HOMEOMORPHIC TO A PRODUCT OF ČECH-COMPLETE SPACES IS A TOPOLOGICAL GROUP

Abstract. A semitopological group (topological group) is a group endowed with a topology for which multiplication is separately continuous (multiplication is jointly continuous and inversion is continuous). In this paper we answer [1, Problem 10.4], by showing that if (G, ·, τ) is a semitopological group and (G, τ) is homeomorphic to a product of Čech-complete spaces, then (G, ·, τ) is a topological group