Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T16:46:34.018Z Has data issue: false hasContentIssue false
  • English
  • Français

Gale transforms and closed faces of infinite dimensional polytopes

Published online by Cambridge University Press:  26 February 2010

P. Kleinschmidt  and
G. R. Wood
P. Kleinschmidt
Affiliation:
Institut für Mathematik der Ruhr-Universität-Bochum, 4630 Bochum, Federal Republic of Germany.
G. R. Wood
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
Get access

Abstract

Gale transforms are constructed for certain infinite dimensional α-polytopes. In a manner analogous to the finite dimensional case the Gale transform can be used to determine all closed faces and Radon partitions of the α-polytope. A by-product is a characterization of closed faces using nets of functionals.

Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 291 - 304
Copyright
Copyright © University College London 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Alfsen, E. M.. Compact convex sets and boundary integrals. Ergebnisse der Math., Vol. 57 (Springer, Berlin, 1971).Google Scholar
2.Alfsen, E. M.. On the geometry of Choquet simplexes. Math. Scand., 15 (1964), 97–110.CrossRefGoogle Scholar
3.Choquet, G.. Lectures on analysis, edited by Marsden, J., Lance, T. and Gelbart, S. (Benjamin, New York, 1969).Google Scholar
4.Ewald, G. and Voss, K.. Konvexe Polytope mit Symmetriegruppe. Comment. Math. Helv., 48 (1973), 137–150.CrossRefGoogle Scholar
5.Grünbaum, B.. Convex polytopes (Interscience, New York, London, Sydney, 1967).Google Scholar
6.McMullen, P.. Transforms, diagrams and representations. In Contributions to Geometry, Proceedings of the Geometry Symposium in Siegen 1978, edited by Tölke, Jürgen and Wills, Jörg M. (Birkhauser, Basel, 1979).Google Scholar
7.Phelps, R. R.. Infinite dimensional compact convex polytopes. Math. Scand., 24 (1969), 5–26.CrossRefGoogle Scholar
8.Rudin, W.. Functional analysis (McGraw-Hill, New York, London, Sydney, 1973).Google Scholar
9.Wood, G. R.. Divisible points of compact convex sets. To appear.Google Scholar