Notes sur la propriété de Namioka

Ahmed Bouziad (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We show that the class of co-Namioka compacts is stable under arbitrary products if and only if it is stable under finite products. We also prove that if $X$ is a Valdivia compact space then for every co-Namioka compact $Y$ the product $X\times Y$ is co-Namioka. Several examples of co-Namioka compacts are given.

Mots clés: separate continuity; joint continuity; Namioka property; Valdivia compactum; Corson compactum

Domaines: Analyse fonctionnelle [math.FA]; Topologie générale [math.GN]

Ahmed Bouziad. Notes sur la propriété de Namioka. Transactions of the American Mathematical Society, 1994, 344 (2), pp.873--883. ⟨hal-00373445⟩