Sperner's Lemma

Karol Pąk

Formalized Mathematics (2010)

  • Volume: 18, Issue: 4, page 189-196
  • ISSN: 1426-2630

Abstract

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In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).

How to cite

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Karol Pąk. "Sperner's Lemma." Formalized Mathematics 18.4 (2010): 189-196. <http://eudml.org/doc/267185>.

@article{KarolPąk2010,
abstract = {In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {189-196},
title = {Sperner's Lemma},
url = {http://eudml.org/doc/267185},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Karol Pąk
TI - Sperner's Lemma
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 4
SP - 189
EP - 196
AB - In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).
LA - eng
UR - http://eudml.org/doc/267185
ER -

References

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