【摘要】 <正> 前言在文[1],[2]中,出于模糊落影理论的需要,引入了几种超拓扑。本文将对其中的一种超拓扑T₂₂（P（X））系统地进行讨论。先把本文所要用到的一些主要符号和术语说明如下:1°/（?）表示集合的包含关系,（?）表示真包含关系。2°（X,T）为拓扑空间。F（X）,T（X）和 H（X）分别表示 X 的闭,开和开闭集类。更多还原

【Abstract】 In [1],the eight kinds of hypertopologies were introduced for the stu- dy of fall-shadow of random sets.The hypertopology T₂₂,one of which is studied in this paper.In this paper,we first introduce a special basis {<V1,…,V_m|U_l,…,U_n>（≠（?））|U_i（i（?）I+n={1,…,n}）and V_j（j（?）I_m={1,…,m}）are all nonempty open sets of X,n≥0 and m≥0}of hypertopology T₂₂（P （X））,where <V_l,…,V_m|U_l,…,U_n>（?）{A（?）P（X）|A°（?）V-j≠（?） and A（?）U_i=（?）,j（?）I_m ={1,…,m},i（?）I_n={1,…,n}},and we study various properties of T₂₂.In this paper,we obtain some important and intresting results: （1）Suppose X is a Hausdorff space,and let R_k（X）（?）{A（?）p（X）||A|≤k and A≠（?）}.Then the natural mapping: p_k:X^k→R_k（X） （X_l,…,X_k）→{x_l,…,X_k} is a continuous mapping（k=1,2,…）. （2）X is a compact space iff T₂₂（（?）P（X））is a compact space,and T₂₂（P（X）） is always compact. （3）Suppose T_l-space X is separable,and let S（X）（?）{A（?）P（X）|A and A° are all separable}.Then （a）S（X）（?）R₁（X）,and further more S（X）（?）R^*（X）U（R^*（X））^\c. （b）X is first countable iff T₂₂（S（X））is first countable. Where R_k^*（X）（?）{A∈P（X）||A|≤k}（k=1,2,…）and R^*（X）（?）R_k^*（X）. （4）If there exists a point which has a countable basis in space T₂₂ （P（X））,then T₂₂（P（X））must be separable.And further more,if X is Haus- dorff space,then T₂₂（_oP（X））is also separable. （5）Suppose X and Y are arbitrary topological space,then П:T₂₂（_oP（X））×T₂₂（_oP（Y））→T₂₂（_oP（X））×_oP（Y）) （A,B）→A×B is a continuous mapping.更多还原