Extreme points in non-positive curvature (Q2835995)
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scientific article; zbMATH DE number 6658334
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extreme points in non-positive curvature |
scientific article; zbMATH DE number 6658334 |
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Extreme points in non-positive curvature (English)
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30 November 2016
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extreme points
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CAT(0) space
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compact convex set
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harmonic series
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The author of this note shows that there exists a bounded complete CAT(0) space without extreme points. Moreover, one can arrange that \(X\) is compact Hausdorf for the convex topology and that every finite collection of points in \(X\) is contained in a finite Euclidean simplicial complex of dimension two. Alternatively, one can construct a CAT(-1) example with hyperbolic simplicial complexes of dimension two.
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