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Topology and its Applications
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Topology and its Applications
Article . 2013
License: Elsevier Non-Commercial
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Topology and its Applications
Article . 2013 . Peer-reviewed
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Article . 2014
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Diagonals of separately continuous functions and their analogs

Authors: Karlova, Olena; Mykhaylyuk, Volodymyr; Sobchuk, Oleksandr;

Diagonals of separately continuous functions and their analogs

Abstract

We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\to Z$ there exists a separately continuous mapping $f:X^2\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.

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Keywords

General Topology (math.GN), FOS: Mathematics, 54C08, 54C05, 26B05, Geometry and Topology, Mathematics - General Topology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
hybrid