Joint continuity of separately continuous mappings

Abstract

In this paper, we will introduce a topological game to show that every separately continuous function f:X×Y→Z, where X is a β-unfavorable space for our game and Z is a regular space, is strongly quasi-continuous at each point of X×{y} provided that y is a q-point. We also show that the set of points of subcontinuity of quasi-continuous mappings from a Baire space X into a regular game determined space Y contains a dense Gδ subset of X. Our results generalize some theorems in Bouziad (1996) [6] and Kenderov et al. (2001) [18].