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Higher Connectedness Properties of Support Points and Functionals of Convex Sets

Published online by Cambridge University Press:  20 November 2018

Carlo Alberto De Bernardi
Carlo Alberto De Bernardi*
Affiliation:
Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy, e-mail: carloalberto.debernardi@gmail.com
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Abstract

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We 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 $\text{AR}$ ( $\sigma $ -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 $X$ .

Keywords

46A5546B9952A07convex setsupport pointsupport functionalabsolute retractLeray-Schauder continuation principle

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 6 , 01 December 2013 , pp. 1236 - 1254
Copyright
Copyright © Canadian Mathematical Society 2013

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