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

Access to Document

10.1007/BF02765904

Cite this

@article{5c5fa4357fb9463d858b08601cb9c1a0,

title = "A combinatorial proof of the Borsuk-Ulam antipodal point theorem",

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.",

author = "Benjamin Weiss",

year = "1989",

month = dec,

doi = "10.1007/BF02765904",

language = "אנגלית",

volume = "66",

pages = "364--368",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "1-3",

}

TY - JOUR

T1 - A combinatorial proof of the Borsuk-Ulam antipodal point theorem

AU - Weiss, Benjamin

PY - 1989/12

Y1 - 1989/12

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/51649154345

U2 - 10.1007/BF02765904

DO - 10.1007/BF02765904

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:51649154345

SN - 0021-2172

VL - 66

SP - 364

EP - 368

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1-3

ER -

A combinatorial proof of the Borsuk-Ulam antipodal point theorem

Abstract

Access to Document

Other files and links

Fingerprint

Cite this