In　this　article,　we　prove　the　existence　of　solutions　for　the　general　variational　inequality　phi(x,　y)　＞=　f(x)　-　f(y)　and　Minty　type　theorem　by　using　the　generalized　KKM　theorem　in　topological　spaces　without　linear　structure.　Some　properties　of　solutions　set　for　the　general　variational　inequality　are　studied　by　Minty　type　theorem.　As　applications,　equivalence　between　Browder　fixed　point　theorem　and　Ky　Fan＇s　minimax　inequality　are　studied　in　topological　spaces.