Continuous Selection Theorems In Generalized Convex Spaces, The Intersection Theorem And Its Applications

This thesis consists of four chapters. At first, we introduce the study history and present situation on continuous selection theory. Secondly, we show continuous selection theorems and fixed point theorems on generalized convex spaces without compactness. By applying continuous selection theorems, we also show collectively fixed point theorems on product generalized convex space. And then, we obtain intersection theorems by using collectively fixed point theorem. At the same time,we also give a proposition equivalent to the intersection theorems. Finally, we give an application to new theorems.This thesis enriches the study results on continuous selection theory and generalizes it. Continuous selection theory can be studied more widely.