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On support points and support functionals of convex sets

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Abstract

Let K be a bounded closed convex subset of a real Banach space of dimension at least two. Then the set of the support points of K is pathwise connected and the set Σ1(K) of the norm-one support functionals of K is uncountable in each nonempty open set that intersects the dual unit sphere. In particular, the set Σ 1(K) is always uncountable, which answers a question posed by L. Zajíček.

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  1. Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50, 20133, Milano, Italy

    C. De Bernardi & L. Veselý

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  1. C. De Bernardi
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  2. L. Veselý
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Correspondence to C. De Bernardi.

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De Bernardi, C., Veselý, L. On support points and support functionals of convex sets. Isr. J. Math. 171, 15–27 (2009). https://doi.org/10.1007/s11856-009-0037-6

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  • DOI: https://doi.org/10.1007/s11856-009-0037-6

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