A classical Lefschetz result about point-finite open covers of normal spaces is generalised by showing that every lower semi-continuous mapping from a normal space into the nonempty compact subsets of a metrizable space admits a closed graph multi-selection. Several applications are given as well.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-1-5,
author = {Valentin Gutev},
title = {Closed graph multi-selections},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {85-99},
zbl = {1239.54010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-1-5}
}
Valentin Gutev. Closed graph multi-selections. Fundamenta Mathematicae, Tome 215 (2011) pp. 85-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-1-5/