Every Needle Point Space Contains a Compact Convex AR-Set with no Extreme Points

DOI10.2307/2160246zbMath0822.54013OpenAlexW4249467492MaRDI QIDQ4290868

Le Hoang Tri, Nguyen To Nhu

Publication date: 5 May 1994

Full work available at URL: https://doi.org/10.2307/2160246

zbMATH Keywords

extreme pointsfixed point propertyHilbert cubecompact convex setsneedle point spaceadmissible convex setAR-set

Mathematics Subject Classification ID

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) (54C55) Local compactness, (sigma)-compactness (54D45)

Related Items (7)

The fixed point property for weakly admissible compact convex sets: Searching for a solution to Schauder's conjecture ⋮ Affine and homeomorphic embeddings into $\ell ^2$ ⋮ The AR-property for Roberts’ example of a compact convex set with no extreme points Part 1: General result ⋮ The AR-property for Roberts’ example of a compact convex set with no extreme points Part 2: Application to the example ⋮ The AR-property in linear metric spaces ⋮ The admissibility and the AR-property of some unbounded convex sets in a class of non-locally convex spaces containing \(l_p\) \((0<p<1)\) ⋮ The Kakutani fixed point theorem for Roberts spaces

Cites Work

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• Shrinkable neighborhoods in Hausdorff linear spaces
• Remarks on measurable function spaces
• A re-examination of the Roberts example of a compact convex set without extreme points
• Separable complete ANR's admitting a group structure are Hilbert manifolds
• The Group of Measure Preserving Transformations of the Unit Interval is an Absolute Retract
• Investigating the ANR-property of metric spaces
• A compact convex set with no extreme points
• On extreme points of regular convex sets

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