
arXiv: 1407.5745
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.
General Topology (math.GN), FOS: Mathematics, 54C08, 54C05, 26B05, Geometry and Topology, Mathematics - General Topology
General Topology (math.GN), FOS: Mathematics, 54C08, 54C05, 26B05, Geometry and Topology, Mathematics - General Topology
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