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Journals / Results in Nonlinear Analysis / 2020 / Cilt: 3 - Sayı: 1

KKM implies the Brouwer fixed point theorem: Another proof

Sehie PARK
Pages
12–17
Publication Date
2020-03-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this article, we recall some KKM theoretic results implying the BFPT.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:It is well-known that the Brouwer fixed point theorem (BFPT), the weak Sperner combinatorial lemma, and the Knaster-Kuratowski-Mazurkiewicz (KKM) theorem are mutually equivalent and have scores of equivalent formulations and several thousand applications.
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Key Findings & Data:It is well-known that KKM deduced the BFPT from Sperner Lemma.
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Conclusion & Impact:In this article, we recall some KKM theoretic results implying the BFPT.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Abstract convex space · KKM space · Brouwer fixed point theorem

Abstract

It is well-known that the Brouwer fixed point theorem (BFPT), the weak Sperner combinatorial lemma, and the Knaster-Kuratowski-Mazurkiewicz (KKM) theorem are mutually equivalent and have scores of equivalent formulations and several thousand applications. It is well-known that KKM deduced the BFPT from Sperner Lemma. In this article, we recall some KKM theoretic results implying the BFPT.

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Cite This Article

PARK, S. (2020). KKM implies the Brouwer fixed point theorem: Another proof. Results in Nonlinear Analysis, Cilt: 3 - Sayı: 1, 12–17. https://ajindex.com/articles/797758

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