On the One-Skeleton of a Compact Convex Set in Banach Spaces. I.
Abstract
Using the max. flow - min. cut theorem, Balinski (1961) proved that any two distinct vertices a, b of a d-dimensional convex polytope can be joined by d paths in the one-skeleton of the convex polytope so that these paths only overlap pairwise in a and b. Here, the author gives a far reaching generalization of this result to infinite dimensional compact convex sets. It is proved that any two distinct exposed points a, b of an infinite dimensional compact convex set can be joined by n simple arcs in the one-skeleton of the set, for any finite a, so that these paths only overlap pairwise at a and b. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1973
- Accession Number
- AD0759067
Entities
People
- David G. Larman
Organizations
- University of Washington