# Construction of Separately Continuous Functions with Given Restriction

### Abstract

We solve the problem of the construction of separately continuous functions on a product of two topological spaces with given restriction. It is shown, in particular, that, for an arbitrary topological space*X*and a function

*g*:

*X*→

**R**of the first Baire class, there exists a separately continuous function

*f*:

*X*×

*X*→

**R**such that

*f*(

*x*,

*x*) =

*g*(

*x*) for every

*x*∈

*X*.

Published

25.05.2003

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 55, no. 5, May 2003, pp. 716-21, https://umj.imath.kiev.ua/index.php/umj/article/view/3947.

Issue

Section

Short communications