Every Čech-analytic Baire semitopological group is a topological group

Ahmed Bouziad (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

This paper answers positively a question of Pfister by proving that every Čech-complete semitopological group (that is, a group with a separately continuous multiplication) is a topological group. In fact, a bit more is proved: every Čech-analytic Baire semitopological group is a topological group. The same result for locally compact groups is known as Ellis's theorem (1957).

Mots clés: Topological group; semitopololgical group; Ellis's theorem; Cech-analytic space; Cech-complete space; separate continuity; joint continuity

Domaines: Topologie générale [math.GN]

Ahmed Bouziad. Every Čech-analytic Baire semitopological group is a topological group. Proceedings of the American Mathematical Society, 1996, 124 (3), pp.953--959. ⟨hal-00373443⟩