Intersection Theorems Under The Restriction Of Semicontinuity On Generalized Convex Spaces With An Application

This thesis consists of five chapters. At first, We introduce the study history as well as present situation on KKM theory. Secondly, We discuss the invariability of transfer open (closed) valued multimap under the restriction of upper and lower semicontinuity on generalized convex spaces. Then, We obtain new KKM type theorems from the classical KKM theorem by applying upper and lower semicontinuity. We also obtain intersection theorems by applying the KKM type theorems for a multimap from a topological space to another topological space. Further, We obtain Ky-Fan type coincidence theorem by applying known variational results on the KKM type theorems. Finally, We give an application to new theorems.This thesis enriches the study results on KKM theory and KKM theory can be studied and applied more widely.