Geodesic
A Note on Minimal Usco Maps
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 412-416

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that the composition of a minimal usco map, defined on a Baire space, with a lower semicontinuous function is single valued and usco at each point of a dense G$ subset of its domain. This extends earlier results of Kenderov and Fitzpatrick. As a first consequence, we prove that a Banach space, with the property that there exists a strictly convex, weak* lower semicontinuous function on its dual, is a weak Asplund space. As a second consequence, we present a short proof of the fact that a Banach space with separable dual is an Asplund space.
DOI : 10.4153/CMB-1991-066-8
Mots-clés : 54C60, 46B22 
Verona, Andrei; Verona, Maria Elena. A Note on Minimal Usco Maps. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 412-416. doi: 10.4153/CMB-1991-066-8
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