中文摘要：

建立集合族空间,讨论了公共元的通有稳定性,得到了闭集族空间上的交运算在Hausdorff拓扑下的上半连续性.在2种拓扑结构下研究了Fan Ky点的通有稳定性,显示了集族空间交运算方法具有良好的适应性.

英文摘要：

A family-of-set space is established.And its common elements’ generic stability is studied.The upper semi-continuity of operation of sets’ intersection in family-of-closed-set space is obtained.And generic stability of Fan Ky point is studied in diverse topology.It has good applicability of the method of sets’ intersection in family-ofclosed-set space.