KKM Theorems on FC-spaces with Their Applications to Variational Inequalities

A new concept of finitely continuous topological spaces (in short, FC-space) without convexity structure and linear structure was introduced. Some KKM type theorems in noncompact FC-spaces were obtained, and from which, some section theorems and variational inequality theorems were proved under much weak assump-tious. Our results improve and generalize the corresponding conclusions in recent literature.