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Higher Connectedness Properties of Support Points and Functionals of Convex Sets
Published online by Cambridge University Press: 20 November 2018
Abstract
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
$X$.
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- Research Article
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- Copyright © Canadian Mathematical Society 2013