An elementary direct proof that the Knaster-Kuratowski-Mazurkiewicz lemma implies Sperner's lemma
General Topology
2017-06-22 v1
Abstract
Three central results in economic theory --- Brouwer's fixed-point theorem, Sperner's lemma, and the Knaster-Kuratowski-Mazurkiewicz (KKM) lemma --- are known to be equivalent. In almost all cases, elementary direct proofs of one of these results using any of the others are easily found in the literature. This seems not to be the case for the claim that the KKM lemma implies Sperner's lemma. The goal of this note is to provide such a proof.
Keywords
Cite
@article{arxiv.1706.06740,
title = {An elementary direct proof that the Knaster-Kuratowski-Mazurkiewicz lemma implies Sperner's lemma},
author = {Mark Voorneveld},
journal= {arXiv preprint arXiv:1706.06740},
year = {2017}
}