We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
@article{bwmeta1.element.bwnjournal-article-fmv149i2p127bwm,
author = {Jan van Mill and Jan Pelant and Roman Pol},
title = {Selections that characterize topological completeness},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {127-141},
zbl = {0861.54016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p127bwm}
}
van Mill, Jan; Pelant, Jan; Pol, Roman. Selections that characterize topological completeness. Fundamenta Mathematicae, Tome 149 (1996) pp. 127-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p127bwm/
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