On the One-Skeleton of a Compact Convex Set in Banach Spaces. I.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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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
- Theoretical Mathematics