The Ellis theorem and continuity in groups

Abstract

Various theorems which are valid in the presence of metrizability or compactness can be generalized to the class of p-spaces. In this paper, we show that this is the case for the classical theorem of Ellis on joint continuity. As an application, we show that the multiplication is continuous in a semitopological Baire group, which is a paracompact p-space; and that, a Čech-complete semitopological group is a topological group if and only if this group is paracompact. A topological game condition, which insures that a group with a continuous multiplication has a continuous inversion is given.