Classification of separately continuous functions with values in $\sigma$-metrizable spaces

TL;DR

This paper proves that certain separately continuous functions with values in strongly σ-metrizable spaces can be approximated pointwise by continuous functions, extending understanding of function limits in topological spaces.

Contribution

It establishes that vertically nearly separately continuous functions into strongly σ-metrizable spaces are pointwise limits of continuous functions, under specific topological conditions.

Findings

Vertically nearly separately continuous functions are pointwise limits of continuous functions.

The results apply to functions with values in strongly σ-metrizable spaces with a special stratification.

The paper extends classical results on function limits to a broader class of topological spaces.

Abstract

We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise limit of continuous functions.