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

KKM implies the Brouwer fixed point theorem: Another proof

Sehie PARK
Sayfa
12–17
Yayın Tarihi
2020-03-31
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:It is well-known that KKM deduced the BFPT from Sperner Lemma.
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Sonuç & Katkı:In this article, we recall some KKM theoretic results implying the BFPT.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (20)

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