A combinatorial proof of the Borsuk-Ulam antipodal point theorem

Benjamin Weiss

doi:10.1007/BF02765904

A combinatorial proof of the Borsuk-Ulam antipodal point theorem

Benjamin Weiss^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We give a proof of Tucker's Combinatorial Lemma that proves the fundamental nonexistence theorem: There exists no continuous map from Bⁿ to S^{n - 1} that maps antipodal points of ∂Bⁿ to antipodal points of S^{n - 1}.

Original language	English
Pages (from-to)	364-368
Number of pages	5
Journal	Israel Journal of Mathematics
Volume	66
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02765904
State	Published - Dec 1989

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abstract = "We give a proof of Tucker's Combinatorial Lemma that proves the fundamental nonexistence theorem: There exists no continuous map from B n to S n - 1 that maps antipodal points of ∂B n to antipodal points of S n - 1.",

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A combinatorial proof of the Borsuk-Ulam antipodal point theorem

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