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Generic continuity of minimal set-valued mappings

Part of: Normed linear spaces and Banach spaces; Banach lattices Calculus on manifolds; nonlinear operators

Published online by Cambridge University Press:  09 April 2009

W. B. Moors  and
J. R. Giles
W. B. Moors
Affiliation:
Department of Mathematics The University of Auckland, New Zealand
J. R. Giles
Affiliation:
Department of Mathematics The University of NewcastleNSW 2308, Australia
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Abstract

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We study classes of Banach spaces where every set-valued mapping from a complete metric space into subsets of the Banach space which satisfies certain minimal properties, is single-valued and norm upper semi-continuous at the points of a dense Gδ subset of its domain. Characterisations of these classes are developed and permanence properties are established. Sufficiency conditions for membership of these classes are defined in terms of fragmentability and σ-fragmentability of the weak topology. A characterisation of non membership is used to show that l∞ (N) is not a member of our classe of generic continuity spaces.

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties 46B20: Geometry and structure of normed linear spaces 58C20: Differentiation theory (Gateaux, Fréchet, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 2 , October 1997 , pp. 238 - 262
Copyright
Copyright © Australian Mathematical Society 1997

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