MAKING NEW KKM SPACES FROM OLD

Abstract

In our previous works [29, 30], we obtained three general KKM type theorems A, B, and C for abstract convex spaces. In a recent work [34], we showed that these three theorems are mutually equivalent. Actually, by adopting a method of making new abstract convex spaces from old, we gave a direct proof of Theorem C from Theorem B. In this paper, we apply our new method to ∅_A-spaces and other spaces appeared in the KKM theory. Especially, we define some new abstract convex spaces called Ψ^l-spaces, Ψ^u-spaces, and Ψ-spaces generalizing ∅_A-spaces.