Construction of separately continuous functions of \(n\) variables with given restriction

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 func...

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Bibliographic Details
Published in:arXiv.org 2016-02
Main Author: Mykhaylyuk, V V
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Mathematical analysis
Topology
Online Access:Get full text
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Summary: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 \(x\in X\).
ISSN:2331-8422