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A Note on Minimal Usco Maps

Published online by Cambridge University Press:  20 November 2018

Andrei Verona  and
Maria Elena Verona
Andrei Verona
Affiliation:
Department of Mathematics, California State University, Los Angeles, CA, USA 90032
Maria Elena Verona
Affiliation:
Department of Mathematics, University of California, Riverside, CA, USA 92521
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Abstract

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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.

Keywords

54C6046B22
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 412 - 416
Copyright
Copyright © Canadian Mathematical Society 1991

References

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