Geometriae Dedicata

, Volume 78, Issue 1, pp 1–19

New Combinations of Convex Sets

  • Peter McMullen

DOI: 10.1023/A:1005019802841

Cite this article as:
McMullen, P. Geometriae Dedicata (1999) 78: 1. doi:10.1023/A:1005019802841


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.

convex set fibre combination polarity convex function convolution. 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Peter McMullen
    • 1
  1. 1.University College LondonLondonEngland

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