Separate Continuity, Joint Continuity, the Lindelof Property and p-spaces

Warren B. Moors


In this paper we prove a theorem more general than the following. Suppose that X
is Cech-complete and Y is a closed subset of a product of a separable metric space
with a compact Hausdorff space. Then for each separately continuous function
f:XxY -> R there exists a residual set R in X such that f is jointly continuous
at each point of RxY. This confirms the suspicions of S.Mercourakis and S.Negrepontis
from 1991.

Separate continuity; Joint continuity; Lindelof Property.

Math Review Classification
Primary 54C05, 22A10 ; Secondary 54E52, 39B99

Last Updated

6 pages

This article is available in: