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On weakly Gibson $F_{σ}$-measurable mappings

100%

Karlova O., Mykhaylyuk V.

Colloquium Mathematicum

2013

tom 133

nr 2

211-219

A function f: X → Y between topological spaces is said to be a weakly Gibson function if $f(Ū) ⊆ \overline{f(U)}$ 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 $F_{σ}$-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 $F_{σ}$-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

81%

Karlova O., Maslyuchenko V., Mykhaylyuk V.

Open Mathematics

2012

tom 10

nr 3

1042-1053

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Karlova O.

2 Mykhaylyuk V.

1 Maslyuchenko V.

1 2013

1 2012

Wyniki wyszukiwania

On weakly Gibson $F_{σ}$-measurable mappings

Equiconnected spaces and Baire classification of separately continuous functions and their analogs