Points of Continuity of Quasi-Continuous Functions

Abstract

We study points of joint continuity of multi-variable 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 set of points of continuity of functions with closed graph into ωΔ-spaces is a Gδ subset of its domain provided that its domain is a W-space.

A Few Variants of Quasi-Continuity in Bitopological Spaces

“…Many results have been obtained for functions as well as for multifunctions. Relevant results can be found in earlier published works [1-3, 5, 10, 11, 13, 15, 18] Recently published works [7,12,14] document the continued interest in quasi-continuity research. We bring to the reader's attention an overview article [16] and a recently published book [6] which summarizes the results devoted to the quasi--continuity of functions and multifunctions from various aspects.…”