关键词: G—FC—KKM定理, S-G—FC—KKM定理, FC一空间

Abstract: A new notion of finite continuous topological space(FC—space)without convexity structure was introduced in 2005． Many topological spaces with abstract convexity structure are all FC—spaces．G—FC—KKM(S-G—FC—KKM)type mappings ale in— troduced．By using the continuous partition of unity theorem，some G—FC—KKM(S-G—FC—KKM)type theorems ale proved in FC—spaces．These theorems generalize some results in recent literature．

Key words: G-FC-KKM theorem, S-G-FC-KKM theorem , FC-spaces