On weakly Gibson $F_{\sigma }$-measurable mappings

Olena Karlova, and Volodymyr Mykhaylyuk. "On weakly Gibson $F_{σ}$-measurable mappings." Colloquium Mathematicae 133.2 (2013): 211-219. <http://eudml.org/doc/284115>.

@article{OlenaKarlova2013,
abstract = {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.},
author = {Olena Karlova, Volodymyr Mykhaylyuk},
journal = {Colloquium Mathematicae},
keywords = {weakly Gibson function; -measurable function; connected graph},
language = {eng},
number = {2},
pages = {211-219},
title = {On weakly Gibson $F_\{σ\}$-measurable mappings},
url = {http://eudml.org/doc/284115},
volume = {133},
year = {2013},
}

TY - JOUR
AU - Olena Karlova
AU - Volodymyr Mykhaylyuk
TI - On weakly Gibson $F_{σ}$-measurable mappings
JO - Colloquium Mathematicae
PY - 2013
VL - 133
IS - 2
SP - 211
EP - 219
AB - 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.
LA - eng
KW - weakly Gibson function; -measurable function; connected graph
UR - http://eudml.org/doc/284115
ER -