Separate and joint continuity in Baire groups

Rok, strany: 1998, 109 - 116

The celebrated theorem of R. Ellis (1957) [R. Ellis: Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125] [R. Ellis: A note on the continuity of the inverse, Proc. Amer. Math. Soc. 8 (1957), 372–373] stating that separately continuous multiplication in a locally compact group is continuous has been generalized by Lawson (1984), G. Hansel and J. P. Troallic (1983) [G. Hansel, J. P. Troallic: Points de continuté a gauche d'une action de semigroupe, Semigroup Forum 26 (1983), 205–214] and D. Helmer (1981) [D. Helmer: Continuity of semigroup actions, Semigroup Forum 23 (1981), 153–188]. A. Bouziad (Topology Appl. (1993)) [A. Bouziad: The Ellis theorem and continuity in groups, Topology Appl. 50 (1993), 73–80] showed that the multiplication is continuous in a semitopological Baire group which is a paracompact $p$-space. He also recently showed (Proc. Amer. Math. Soc. (1996)) that the multiplication is continuous in semitopological Čech-complete groups. We shall prove (Theorem 5) that if $X$ is a Baire, Moore semitopological group, then $X$ is paratopological.

ISO 690:

Piotrowski, Z. 1998. Separate and joint continuity in Baire groups. In Tatra Mountains Mathematical Publications, vol. 14, no.1, pp. 109-116. 1210-3195.

APA:

Piotrowski, Z. (1998). Separate and joint continuity in Baire groups. Tatra Mountains Mathematical Publications, 14(1), 109-116. 1210-3195.