Some results on nearest points and support properties of convex sets in c₀

M. Edelstein and Anthony Charles Thompson

Vol. 40 (1972), No. 3, 553–560

DOI: 10.2140/pjm.1972.40.553

Abstract

The space c₀ is shown to contain a closed and bounded symmetric convex body such that no point of its complement has a nearest point in it. Related results involving the existence of functionals which support each member of a family of convex sets are also discussed.

Mathematical Subject Classification

Primary: 46B05

Milestones

Received: 19 August 1970

Published: 1 March 1972