Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Victor Klee

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

Klee@math.washington.edu

Elisabetta Maluta

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

elimal@mate.polimi.it

Clemente Zanco

Dip. di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy

zanco@mat.unimi.it

Keywords

  • Evenly convex set
  • evenly convex cone
  • section
  • projection

Mathematics Subject Classification

52A20, 15A39

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Suggested citation

V. Klee, E. Maluta, C. Zanco. “Basic Properties of Evenly Convex Sets.” Journal of Convex Analysis 14 (2007), No. 1, 137–148. https://doi.org/10.68381/jca14011

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.