Semitopological group

Summary

A semitopological group is a group with a topology in which multiplication is continuous in each variable separately. Equivalently, every left translation and every right translation is continuous, and then each translation is a homeomorphism. It weakens the notion of a topological group, which asks for joint continuity of multiplication and continuity of inversion. Ellis's theorem says that a locally compact Hausdorff semitopological group is already a topological group.