关键词: R-KKM映射, R-子集, 转移开［闭］值映射, 上半连续, 极大元

Abstract: KKM type of theorem in general topological space without any convexity structure was obtained, from which we obtain many fixed point theorems or existence theorem of maximal element for FanBrowder type map in noncompact general topological space without any convexity structure.

Key words: R-KKM map, R-subset, transfer open ［closed］ valued map, upper semicontinuous, maximal element