Maximal element theorems in product FC-spaces and generalized games

Let I be a finite or infinite index set, X be a topological space and (Yi , {ϕNi })i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i ∈ I, let Ai :X →2Yi be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai } i∈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.  2004 Elsevier Inc. All rights reserved.