On the Existence of Greatest and Maximal Elements

The main purpose of this paper is to deal with the existence of greatest and maximal elements of weak and strict preference relations and give necessary conditions for the existence of greatest and maximal elements of weak and strict preference relations in framework of general topological spaces without linear and convex structure. The well known KKM theorem is applied to proving the existence theorem of greatest and maximal elements of weak and strict preference relations under mild conditions.