Maximal element theorems in product FC-spaces and generalized games

Let 1 be a finite or infinite index set, X be a topological space and (Y-i, {phi(Ni)})i epsilon be a family of finitely continuous topological spaces (in short, FC-space). For each i epsilon I, let A(i) : X -> 2(Yi) be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}i epsilon I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature. (c) 2004 Elsevier Inc. All rights reserved.