Construction of separately continuous functions of $n$ variables with given restriction

V. V. Mykhaylyuk

Construction of separately continuous functions of $n$ variables with given restriction

General Topology 2016-02-02 v1

Authors: V. V. Mykhaylyuk

Abstract

It is solved the problem on construction of separately continuous functions on product of $n$ topological spaces with given restriction. In particular, it is shown that for every topological space $X$ and $n-1$ 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 $x\in X$ .

Keywords

separately continuous functions product of topological spaces Baire class function restriction topology n variables function construction

Cite

@article{arxiv.1602.00452,
  title  = {Construction of separately continuous functions of $n$ variables with given restriction},
  author = {V. V. Mykhaylyuk},
  journal= {arXiv preprint arXiv:1602.00452},
  year   = {2016}
}

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