The rise and fall of MC-spaces

Year 2021, Volume: 4 Issue: 1, 21 - 32, 31.03.2021

Sehie Park

https://doi.org/10.53006/rna.852462

Abstract

In 1994, Llinares introduced mc-spaces and began to study KKM theoretic results on them. Since 1998, he became an L-space theorist and repeated to claim that his mc-spaces generalize G-convex spaces without any justifications. Later he insisted that his mc-spaces are the same as L-spaces. Hence his study on mc-spaces is
useless now as the L-space case shown by our previous works. The present article is a continuation of our previous works on L-spaces and concerns with the rise and fall of mc-spaces. This paper will be an important record for the history of the KKM theory.

Keywords

KKM theorem, Fan's 1961, G-convex space, KKM lemma, (partial) KKM space, mc-space, abstract convex space, L-space

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