Sur les convexes ubiquitaires

G. Coquet and J. C. Dupin

Vol. 57 (1975), No. 1, 67–84

DOI: 10.2140/pjm.1975.57.67

Abstract

In this paper we develop and generalize some previously announced results concerning ubiquitous convex sets. We show two conditions which are sufficient to assert that a convex set which is ubiquitous-elementary or ubiquitous-basic is also linearly bounded. In showing the essential part played by the ubiquitous convex sets of countable infinite dimension we establish that in an infinite-dimensional real vector space every ubiquitous convex set contains a linearly bounded ubiquitous convex set of a specific type.

Mathematical Subject Classification 2000

Primary: 46A99

Secondary: 52A05

Milestones

Received: 12 June 1974

Published: 1 March 1975