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A Remark on Convex Polytopes

Published online by Cambridge University Press:  20 November 2018

A. S. Glass
A. S. Glass*
Affiliation:
University of British Columbia
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In this note we wish to present an alternative proof for the following well-known theorem [1, Theorem 16]: every convex polytope X in Euclidean n-dimensional space Rn is the intersection of a finite family of closed half-spaces. It will be supposed that the converse of this theorem has been verified by conventional arguments, namely: every bounded intersection of a finite family of closed half-spaces in Rn is a convex polytope [cf. 1, Theorem 15].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 829 - 830
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Eggleston, H. G., "Convexity", (Cambridge, 1958).Google Scholar