Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658973 | Topology and its Applications | 2013 | 8 Pages |
Abstract
We prove that for a topological space X, an equiconnected space Z and a Baire-one mapping g:X→Z there exists a separately continuous mapping f:X2→Z with the diagonal g, i.e. g(x)=f(x,x) for every x∈X. Under a mild assumptions on X and Z we obtain that diagonals of separately continuous mappings f:X2→Z are exactly Baire-one functions, and diagonals of mappings f:X2→Z which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology