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Martini, Horst; Wenzel, Walter : An analogue of the Krein-Milman Theorem for star-shaped sets

Martini, Horst ; Wenzel, Walter : An analogue of the Krein-Milman Theorem for star-shaped sets

Author(s):
Martini, Horst
Wenzel, Walter
Title:
An analogue of the Krein-Milman Theorem for star-shaped sets
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 4, 2001
Mathematics Subject Classification:
06A15 [ Galois correspondences, closure operators ]
52-01 [ Instructional exposition (textbooks, tutorial papers, etc.) ]
52A20 [ Convex sets in $n$ dimensions (including convex hypersurfaces) ]
52A30 [ Variants of convex sets (star-shaped, ($m, n$)-convex, etc.) ]
Abstract:
If $S \subseteq R^n$ is compact and star-shaped, we consider a fixed, nonempty, compact and convex subset K of the convex kernel of S. We prove that $\sigma(sol=S\backslash K$, where $\sigma : \rho(R^n \backslash K) \rightarrow \rho(R^n \backslash T)$ denotes same closure operator induced by visibility problems, and so denotes the - appropriately defined - set of extreme points of S modula K
Keywords:
convex sets, star-shaped sets, closure operators, Krein-Milman theorem, visibility problems, d- dimensional volume
Language:
English
Publication time:
11 / 2001