Topological games and topological groups

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 give some topological conditions on a semitopological group that imply that it is a topological group. In particular, we show that every almost Čech-complete semitopological group is a topological group. Thus we improve some recent results of A. Bouziad.