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) : Larman,David G.

Report Date : MAR 1973

Pagination or Media Count : 39

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)

Descriptors :   (*CONVEX SETS, BANACH SPACE), VECTOR SPACES, TOPOLOGY, TRANSFORMATIONS(MATHEMATICS), INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE