New Combinations of Convex Sets
- Peter McMullen
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The family of convex sets in a (finite dimensional) real vector space admits several unary and binary operations – dilatation, intersection, convex hull, vector sum – which preserve convexity. These generalize to convex functions, where there are in fact further operations of this kind. Some of the latter may be regarded as combinations of two such operations, acting on complementary subspaces. In this paper, a general theory of such mixed operations is introduced, and some of its consequences developed.
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- New Combinations of Convex Sets
Volume 78, Issue 1 , pp 1-19
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- Kluwer Academic Publishers
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- convex set
- fibre combination
- convex function
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- Peter McMullen (1)
- Author Affiliations
- 1. University College London, Gower Street, London, WC1E 6BT, England