Generalizations of Hyperconvex Metric Spaces

Abstract

Since Khamsi found a KKM theorem for hyperconvex metric spaces in 1996, there have appeared a large number of works on them related to the KKM theory. In our previous review [34], we followed the various stages of developments of the KKM theory of hyperconvex metric spaces. In fact, we introduced abstracts of articles on such theory and gave comments or generalizations of the results there if necessary. We noted that many results in those articles are consequences of (partial) KKM space theory developed by ourselves from 2006. The present survey is a continuation of [34] and aims to collect further generalizations of hyperconvex metric spaces related to the KKM theory.

Keywords

• abstract convex space; horvath space
• metric type space
• metric spaces with continuous midpoints
• global nonpositive curvature (npc)