From KKM Class to KC Class of Multimaps

Sehie Park

From KKM Class to KC Class of Multimaps

Authors

Sehie Park The National Academy of Sciences, Republic of Korea; Seoul 06579 and Department of Mathematical Sciences, Seoul National University, Seoul 08826, Korea

Keywords:

Abstract convex space, KKM theorem, KKM class of multimaps, \mathfrak{A}_c^\kappa, \mathfrak{B}, \mathfrak{K}, \mathfrak{KC}, \mathfrak{KO}

Abstract

This is to give a short history of our multimap classes $\mathfrak{K,\ KC,\ KO}$ in the KKM theory. We show that many authors adopted or imitated the inadequate definition of the KKM class due to Chang and Yen in 1996. We list such works in chronological order and also introduce other works which extended the class properly. Our study on such history will improve the KKM theory in the new millennium.