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Two-dimensional convexities are join-hull commutative

By M. Van De Vel


AbstractIt is shown that two-dimensional convex structures with certain natural properties are join-hull commutative. The main intermediate step is the computation of the so-called exchange number. We also give two examples of three-dimensional convexities which are not join-hull commutative. The second one has certain additional properties showing that the main theorem is sharp in many other respects. These properties are obtained from a study of convex hyperspaces

Publisher: Published by Elsevier B.V.
Year: 1983
DOI identifier: 10.1016/0166-8641(83)90018-4
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