The Ellis theorem and continuity in groups

Ahmed Bouziad (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 Cech-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.

Domaines: Topologie générale [math.GN]

Ahmed Bouziad. The Ellis theorem and continuity in groups. Topology and its Applications, 1993, 50 (Issue 1), pp.73-80. ⟨hal-00373431⟩