Borsuk-Ulam type theorems for metric spaces

2012/09/06 by Arseniy Akopyan, Akopyan, Arseniy, Роман Карасев +3 · 1 citation
Mathematics · #51F99 #53C23 #55M20 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1209.1249

openalex publication_date 2012/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the problems of the following kind: For a pair of topological spaces X and Y find sufficient conditions that under every continuous map f : X→ Y a pair of sufficiently distant points is mapped to a single point.

Citations

• On Gromov's Waist of the Sphere Theorem

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• An optimal Brouwer's fixed point theorem for discontinuous functions

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