A parametric type of KKM theorem in FC-spaces with applications

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures. Project supported by the National Natural Science Foundation of China (No. 10771173) and the Natural Science Foundation Project of CQ CSTC (No. 2005BB2097)