Any semitopological group that is homeomorphic to a product of Čech-complete spaces is a topological group (Q2436678)

The main result of the paper gives sufficient topological conditions that ensure that a semitopological group is a topological one. These conditions involve two notions that are introduced via the framework of topological games, namely that of nearly strongly Baire spaces, respectively, of nearly \(q_D\)-points. It is shown that if \(G\) is a semitopological group, which is (as a topological space) nearly strongly Baire, and if \(D\) is a dense subset of \(G\) such that the identity element of \(G\) is a nearly \(q_D\)-point, then \(G\) is a topological group. A consequence of this result states that a semitopological group that is (as a topological space) homeomorphic to a product of Čech-complete spaces, is a topological group.