The following known selection theorem is sharpened, primarily, by weakening the hypothesis that all the sets φ(x) are closed in Y: Let X be paracompact with dimX = 0, let Y be completely metrizable and let φ:X → 𝓕(Y) be l.s.c. Then φ has a selection.
@article{bwmeta1.element.bwnjournal-article-fmv140i3p279bwm,
author = {B. Michael},
title = {Some refinements of a selection theorem with O-dimensional domain},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {279-287},
zbl = {0763.54015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv140i3p279bwm}
}
Michael, B. Some refinements of a selection theorem with O-dimensional domain. Fundamenta Mathematicae, Tome 141 (1992) pp. 279-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i3p279bwm/
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