Improving some KKM theoretic results

Year 2020, Volume: 3 Issue: 2, 68 - 77, 30.06.2020

Sehie Park

Abstract

The purpose of this article is to introduce some works on the KKM theory which can be improved according to our theory on abstract convex spaces. In Section 2, we introduce some basic things on our abstract convex spaces as a preliminary. Section 3 deals with the basic results and subjects of our study on the KKM theory. In Section 4, we introduce several works that appeared since 2010. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work and add some comments showing how to improve them.

Keywords

Abstract convex space, KKM theorem, KKM space, mapping classes $\mathfrak{KC}$, $\mathfrak{KO}$

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