Higher Connectedness Properties of Support Points and Functionals of Convex Sets
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Published:2013-12-01
Issue:6
Volume:65
Page:1236-1254
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ISSN:0008-414X
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Container-title:Canadian Journal of Mathematics
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language:en
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Short-container-title:Can. j. math.
Author:
De Bernardi Carlo Alberto
Abstract
AbstractWe prove that the set of all support points of a nonempty closed convex bounded set C in a real infinite-dimensional Banach space X is AR(σ-compact) and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals of C and for the domain, the graph, and the range of the subdifferential map of a proper convex lower semicontinuous function on X.
Publisher
Canadian Mathematical Society
Subject
General Mathematics