Construction of separately continuous functions with given restriction

V. V. Mykhaylyuk

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arXiv · 1601.07984

Construction of separately continuous functions with given restriction

V. V. Mykhaylyuk

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Abstract

It is solved the problem on constructed of separately continuous functions on product of two topological spaces with given restriction. In particular, it is shown that for every topological space $X$ and first Baire class function $g:X\to \bf R$ there exists separately continuous function $f:X\times X \to \bf R$ such that $f(x,x)=g(x)$ for every $x\in X$.

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V. V. Mykhaylyuk. 2016-01-29. Construction of separately continuous functions with given restriction. https://arxiv.org/abs/1601.07984

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