Accession Number:

AD0759067

Title:

On the One-Skeleton of a Compact Convex Set in Banach Spaces. I.

Descriptive Note:

Technical rept.,

Corporate Author:

WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1973-03-01

Pagination or Media Count:

39.0

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

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE