Using volume to prove Sperner's Lemma

DOI10.1007/s00199-007-0257-0zbMath1139.51008OpenAlexW2057073456WikidataQ124802747 ScholiaQ124802747MaRDI QIDQ926230

Rabee Tourky, Andrew McLennan

Publication date: 26 May 2008

Published in: Economic Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00199-007-0257-0

zbMATH Keywords

Brouwer's fixed point theoremSperner's lemmaLebesgue measure

Mathematics Subject Classification ID

Combinatorial geometries and geometric closure systems (51D20)

Related Items (4)

Proving Tucker’s Lemma with a volume argument ⋮ Proofs (not) from The Book ⋮ Envy-free cake division without assuming the players prefer nonempty pieces ⋮ The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

Cites Work

• Combinatorial analogs of Brouwer's fixed-point theorem on a bounded polyhedron
• Simplicial algorithms on the simplotope
• A polytopal generalization of Sperner's lemma
• Analytic Proofs of the "Hairy Ball Theorem" and the Brouwer Fixed Point Theorem
• Lectures on Polytopes
• The Approximation of Fixed Points of a Continuous Mapping
• On the Sperner lemma
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