Polyhedrality of infinite dimensional cubes

Thomas E. Armstrong

Vol. 70 (1977), No. 2, 297–307

DOI: 10.2140/pjm.1977.70.297

Abstract

There are several definitions of polyhedrality for infinite dimensional convex sets. We consider each of these in turn and ask whether infinite dimensional cubes are examples. We find that only the concept of polyhedrality put forth by Alfsen and Nordseth admits infinite dimensional cubes as examples. In some sense this concept of polyhedrality is singled out as the only one which properly generalizes the finite dimensional notion of polyhedrality.

Mathematical Subject Classification 2000

Primary: 46A99

Secondary: 46B99, 52A05

Milestones

Received: 20 April 1976

Published: 1 June 1977