Ukrainian Mathematical Bulletin

Volume 3, Issue 3, 2006 pp. 361-368.

Construction of Separately Continuous Functions of $n$ Variables with Given Restrictions

Authors: Volodymyr V. Mykhaylyuk
Author institution: Chernivtsi Yuri Fed'kovych National University, vul. Kotsyubyns'kogo, 2, 58012, Chernivtsi, Ukraine, mathan@chnu.cv.ua

Summary: We solve the problem of constructing separately continuous functions on the product of $n$ topological spaces with a given restriction. In particular, it is shown that for an arbitrary topological space $X$ and an $(n-1)$ Baire class function $g:X\to\mathbb R$ there exists a separately continuous function $f:X^n\to\mathbb R$ such that $f(x,x,\dots,x)=g(x)$ for every $x\in X$.

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