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

• Autorzy: Olena Karlova , Volodymyr Mykhaylyuk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26A21: Classification of real functions; Baire classification of sets and functions
• 26B05: Continuity and differentiation questions
• 54C08: Weak and generalized continuity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 2
• Strony: 211-219

Daty

wydano

2013

Twórcy

autor

Olena Karlova

• Chernivtsi National University, Department of Mathematical Analysis, 58012 Chernivtsi, Ukraine

autor

Volodymyr Mykhaylyuk

• Chernivtsi National University, Department of Mathematical Analysis, 58012 Chernivtsi, Ukraine

Identyfikatory

DOI

10.4064/cm133-2-7