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.
Basic properties of evenly convex sets / V. Klee, E. Maluta, C. Zanco. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 14:1(2007), pp. 137-148.
Basic properties of evenly convex sets
C. ZancoUltimo
2007
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.
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