The AR-property for Roberts’ example of a compact convex set with no extreme points Part 1: General result

DOI10.1090/S0002-9939-97-04020-3zbMath0890.54015OpenAlexW1567808568MaRDI QIDQ4356721

Tran Van An, Nguyen To Nhu, Jose M. Rodriguez Sanjurjo

Publication date: 1 October 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-04020-3

zbMATH Keywords

extreme pointlinear metric spaceconvex setabsolute retract

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 (3)

The AR-property in linear metric spaces ⋮ Open problems in topology, seventh status report ⋮ The Kakutani fixed point theorem for Roberts spaces

Cites Work

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• Shrinkable neighborhoods in Hausdorff linear spaces
• Leray-Schauder theory without local convexity
• A re-examination of the Roberts example of a compact convex set without extreme points
• No Roberts space is a counter-example to Schauder's conjecture
• Some Applications of The Topological Characterizations of the Sigma-Compact Spaces l 2 f and &#8721
• Investigating the ANR-property of metric spaces
• A compact convex set with no extreme points
• Every Needle Point Space Contains a Compact Convex AR-Set with no Extreme Points
• The Compact Neighborhood Extension Property and Local Equi-Connectedness
• The Finite Dimensional Approximation Property and the AR-Property in Needle Point Spaces
• On extreme points of regular convex sets

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