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Journal of Convex Analysis 22 (2015), No. 3, 889--900
Copyright Heldermann Verlag 2015



On Constant Width Sets in Hilbert Spaces and Around

Luigi Caspani
Dip. di Matematica "F. Enriques", UniversitÓ degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
luigi.caspani@gmail.com

Pier Luigi Papini
Dip. di Matematica, UniversitÓ di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
pierluigi.papini@unibo.it



We present some results concerning the family CW of sets with constant width and the family DM of diametrically maximal (or diametrically complete) sets. In particular we prove (Theorem 2) that CW = DM in Hilbert spaces.

Keywords: Constant width, diametrically maximal sets, arcs.

MSC: 52A05; 52A21, 46B99

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