On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
On weakly Gibson -measurable mappings
A function f: X → Y between topological spaces is said to be a weakly Gibson function if for any open connected set U ⊆ X. We prove that if X is a locally connected hereditarily Baire space and Y is a T₁-space then an -measurable mapping f: X → Y is weakly Gibson if and only if for any connected set C ⊆ X with dense connected interior the image f(C) is connected. Moreover, we show that each weakly Gibson -measurable mapping f: ℝⁿ → Y, where Y is a T₁-space, has a connected graph.
Equiconnected spaces and Baire classification of separately continuous functions and their analogs
We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable.
Diagonals of separately continuous functions of variables with values in strongly -metrizable spaces
We prove the result on Baire classification of mappings which are continuous with respect to the first variable and belongs to a Baire class with respect to the second one, where is a -space, is a topological space and is a strongly -metrizable space with additional properties. We show that for any topological space , special equiconnected space and a mapping of the -th Baire class there exists a strongly separately continuous mapping with the diagonal . For wide classes of spaces...
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