The rise and fall of MC-spaces

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