Quasicontinuous and separately continuous functions with values in Maslyuchenko spaces

TL;DR

This paper extends classical results on quasicontinuous and separately continuous functions to Maslyuchenko spaces, exploring their properties and relationships with other generalized metric spaces, and analyzing discontinuity sets in product spaces.

Contribution

It introduces Maslyuchenko spaces, studies their stability and relation to known classes, and proves that discontinuity sets have meager projections in certain product spaces.

Findings

Discontinuity set projections are meager in specific product spaces.

Maslyuchenko spaces generalize classical metric space results.

Stability properties of Maslyuchenko spaces are established.

Abstract

We generalize some classical results about quasicontinuous and separately continuous functions with values in metrizable spaces to functions with values in certain generalized metric spaces, called Maslyuchenko spaces. We establish stability properties of the classes of Maslyuchenko spaces and study the relation of these classes to known classes of generalized metric spaces (such as Piotrowski or Stegall spaces). One of our results says that for any $\aleph_0$-space $Z$ and any separately continuous function $f:X\times Y\to Z$ defined on the product of a topological space $X$ and a second-countable space $Y$, the set $D(f)$ of discontinuity points of $f$ has meager projection on $X$.