An elementary direct proof that the Knaster–Kuratowski–Mazurkiewicz lemma implies Sperner’s lemma

Mark Voorneveld

Economics Letters, 2017, vol. 158, issue C, 1-2

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: Knaster–Kuratowski–Mazurkiewicz; Sperner; Brouwer (search for similar items in EconPapers)
JEL-codes: C62 C69 (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0165176517302409
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:158:y:2017:i:c:p:1-2

DOI: 10.1016/j.econlet.2017.06.013

Access Statistics for this article

Economics Letters is currently edited by Economics Letters Editorial Office

More articles in Economics Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().