Geodesic
Selections that characterize topological completeness
Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 127-141

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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].
DOI : 10.4064/fm-149-2-127-141
Keywords: selection, Vietoris topology, completely metrizable

Jan van Mill 1 ; Jan Pelant 1 ; Roman Pol 1

1 
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Jan van Mill; Jan Pelant; Roman Pol. Selections that characterize topological completeness. Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 127-141. doi: 10.4064/fm-149-2-127-141

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