A note on spaces related to Namioka spaces

Abstract

Namioka proved that the following condition (*) given below holds, if X is Čech-complete and Y is a locally compact, σ-compact space.(*) Let X and Y be spaces, Z be a metric space and let f: X × Y → Z be separately continuous. Then there is a dense, Gδ set A in X such that A × Y ⊂ C(f).Following Christensen a space X is called Namioka if (*) is true for any compact space Y. In this paper we introduce and study a new class of spaces which is closely related to Namioka spaces. Namely, we say that a space Y is co-Namioka if (*) holds for any Namioka space X.