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Journal of Convex Analysis 14 (2007), No. 1, 137--148
Copyright Heldermann Verlag 2007

Basic Properties of Evenly Convex Sets

Victor Klee
Dept. of Mathematics, University of Washington, Box 354350, Seattle, WA 98195-4350, U.S.A.

Elisabetta Maluta
Dip. di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

Clemente Zanco
Dip. di Matematica, UniversitÓ degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

A subset of a finite-dimensional real vector space is called evenly convex if it is the intersection of a collection of open halfspaces. The study of such sets was initiated in 1952 by Werner Fenchel, who defined a natural polarity operation and mentioned some of its properties. Over the years since then, evenly convex sets have made occasional appearances in the literature but there has been no systematic study of their basic properties. Such a study is undertaken in the present paper.

Keywords: Evenly convex set, evenly convex cone, section, projection.

MSC: 52A20, 15A39

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