【摘要】 基于无穷局部连通的紧致度量空间X到Hilbert方体Q=[0,1]ω的连续函数族C(X,Q)作为乘积空间X×Q的闭子集组成的超空间Cld(X×Q)的子空间,讨论连续函数超空间C(X,Q)及其在Cld(X×Q)中的闭包C(X,Q)的拓扑结构,得到(C(X,Q),C(X,Q))对同胚于(Q,s).更多还原

【Abstract】 Based on the thought that the family of all the continuous functions from an infinite,locally connected compact,metrizable space X to Hilbert cube Q=ω is regarded as a subspace of the hyperspace CldX×Q of closed subsets to the product space X×Q,we discuss the topological structures of C(X,Q) and its closure C(X,Q) in CldX×Q,moreover,we have(C(X,Q),C(X,Q))≈(Q,s).更多还原