The fixed point property for weakly admissible compact convex sets: Searching for a solution to Schauder's conjecture

DOI10.1016/0166-8641(94)00022-0zbMath0848.47038OpenAlexW1997204408MaRDI QIDQ1910705

Nguyen To Nhu

Publication date: 16 October 1996

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(94)00022-0

zbMATH Keywords

AR-propertyfixed point propertyweakly admissiblecompact convex

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Pathological topological spaces (54G15) Fixed-point theorems (47H10) Convex sets in topological linear spaces; Choquet theory (46A55)

Related Items

Fixed Point Theorem and Related Nonlinear Analysis by the Best Approximation Method in p-Vector Spaces, Topological results, Rothe's principle and Leray-Schauder alternative for the fixed point equation in \(p\)-vector spaces, Nonlinear analysis in \(p\)-vector spaces for single-valued 1-set contractive mappings, Fixed points for convex continuous mappings in topological vector spaces, Fixed point theorem in subsets of topological vector spaces, Nonlinear analysis by applying best approximation method in \(p\)-vector spaces, 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
• Regular retractions onto finite dimensional convex sets and the AR-property for Roberts spaces
• On Riemann integration of functions with values in topological linear spaces
• A Rigid Subspace of L 0
• A compact convex set with no extreme points
• Every Needle Point Space Contains a Compact Convex AR-Set with no Extreme Points
• The AR-property for Roberts’ example of a compact convex set with no extreme points Part 2: Application to the example
• The Finite Dimensional Approximation Property and the AR-Property in Needle Point Spaces