Every Čech-analytic Baire semitopological group is a topological group
Résumé
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).