连续函数超空间

Hyperspaces of Continuous Functions

基于空间X到空间Y的连续函数族作为乘积空间X×Y的闭子集组成的超空间CL(X×Y)的子空间 ,在限制Y为Hilbert方体Q时 ,得到连续函数超空间C(X ,Q)同胚于Q的伪内部s;在限制X为单位闭区间I时 ,考虑连续函数超空间C(I,Y)在CL(I×Y)中的闭包 ,得到其元素到Y的投影是连续统 ,且投影随I中的点连续变化 ,并举例说明了即使X为单位圆盘 ,上述第二个结论也不能成立 .

Let X and Y be spaces.We use CL(X×Y)to denote the hyperspace of all non-empty closed subsets in product space X×Y and C(X,Y)which can be regarded as the subspace of CL(X×Y).This paper studied under the fixed conditions of X and Y the respective and relative topological structures of C(X,Y),and the closures of C(X,Y) and CL(X×Y).