Vol. 35, No. 1, 1970

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Caratheodory theorems in convex product structures

John Robert Reay

Vol. 35 (1970), No. 1, 227–230

Various attempts have been made to place convexity in an axiomatic setting. Recently J. Eckhoff has considered the classic theorem of Radon in several different settings. Most of his work is done in what we call an Eckhoff space, i.e., in a finite product of euclidean spaces where convex sets are defined as the cartesian products of usual convex sets in each component space. The purpose of this paper is to investigate the closely related theorem of Caratheodory and its generalizations in this setting.

Mathematical Subject Classification
Primary: 52.30
Received: 16 October 1969
Published: 1 October 1970
John Robert Reay