Topologizing Sperner's lemma

The aim of this paper is to extend Sperner's lemma for a new class of complexes, called $n$-Sperner. Next, we consider a topological version of Sperner's lemma, which leads to characterization of the covering dimension and KKM-principle. Finally, for an arbitrary topological space a new dimension is defined.

Authors

Publication Details

Journal
Topological Methods in Nonlinear Analysis
Published
2024-09-21
DOI
https://doi.org/10.12775/tmna.2024.008
Citations
1
Primary Topic
History and Theory of Mathematics
Type
article
Field-Weighted Citation Impact
7.18
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article

Topologizing Sperner's lemma

Przemysław Tkacz
1 citations
Topological Methods in Nonlinear Analysis
History and Theory of Mathematics
7.18
article

Topologizing Sperner's lemma

Przemysław Tkacz
article en
1 citations

Abstract

The aim of this paper is to extend Sperner's lemma for a new class of complexes, called $n$-Sperner. Next, we consider a topological version of Sperner's lemma, which leads to characterization of the covering dimension and KKM-principle. Finally, for an arbitrary topological space a new dimension is defined.

Topological Methods in Nonlinear Analysis
Openalex Percentile: Top 5%
History and Theory of Mathematics
7.18
DOIOpen Access PDFOpenAlex
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Topologizing Sperner's lemma — Przemysław Tkacz · Topological Methods in Nonlinear Analysis (2024) | TGRS Research Map | TGRS