Vol. 57, No. 1, 1975

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Sur les convexes ubiquitaires

G. Coquet and J. C. Dupin

Vol. 57 (1975), No. 1, 67–84

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
Received: 12 June 1974
Published: 1 March 1975
G. Coquet
J. C. Dupin