Points of continuity of quasi-continuous functions

Abstract

We study points of joint continuity of multi-variable functions separately quasi-continuous functions which are continuous with respect to one variable. We will show that the assumption of complete regularity in the paper of V. Maslyuchenko et al in  ''Tatra Mt. Math. Pub. 68, (2017), 47--58" can be removed  in some situations.  Moreover, we use a topological game argument to prove that the points of  continuity of functions with closed graph into $w\Delta$-spaces is a $G_\delta$ subset of its domain provided that its domain is a $W$-space.