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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-7,
author = {Olena Karlova and Volodymyr Mykhaylyuk},
title = {On weakly Gibson $F\_{$\sigma$}$-measurable mappings},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {211-219},
zbl = {1285.26024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-7}
}
Olena Karlova; Volodymyr Mykhaylyuk. On weakly Gibson $F_{σ}$-measurable mappings. Colloquium Mathematicae, Tome 131 (2013) pp. 211-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-7/