ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 54C05, 54C30, 26A15 Šostak, Alexander, University of Latvia, Riga, Latvia; Szymanski, Andrzej, Slippery Rock University, Pennsylvania, USA On a class of special Namioka spaces Following [HJT], a space X is called Namioka space if for every separately continuous function f : X×Y → M where Y is compact and M metric there exists a dense G_{δ} A ⊂ X s. t. f is continuous at each point of A × Y. X is called a special Namioka if each its perfect irreducible preimage is Namioka. Theorem Any Baire strict p-space is special Namioka. Corollary (cf [SR]) Metric Baire spaces are special Namioka Corollary Let (G, +) be a group endowed with a topology which is Baire and Moore and such that + is separately continuous. Then + is jointly continuous. References: [HJT] R. Hansel, J. Jayne, M. Talagrand, First class selectors. .. , J. Reine Ungewandte Mathematik, 361 (1985), 201-220. [SR] J. Saint Raymond, Jeux topologique et espaces de Namioka, Proc. Amer. Math. Soc. 87 (1983), 499-504.