For a Tychonoff space X, we use ↓USCF（X） and↓CF（X） to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0, 1] with the subspace topologies of the hypersp...For a Tychonoff space X, we use ↓USCF（X） and↓CF（X） to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0, 1] with the subspace topologies of the hyperspace Cldf（X × I） consisting of all non-empty closed sets in X × I endowed with the Fell topology. In this paper, we shall show that there exists a homeomorphism h： ↓USCF（X） → Q = [-1, 1]^∞ such that h（↓ CF（X）） ： co ： {（Xn） E Q ｜ limn→ ∞ xn = O} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X.展开更多
基金Supported by National Natural Science Foundation of China (Grant No.10971125)
文摘For a Tychonoff space X, we use ↓USCF（X） and↓CF（X） to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0, 1] with the subspace topologies of the hyperspace Cldf（X × I） consisting of all non-empty closed sets in X × I endowed with the Fell topology. In this paper, we shall show that there exists a homeomorphism h： ↓USCF（X） → Q = [-1, 1]^∞ such that h（↓ CF（X）） ： co ： {（Xn） E Q ｜ limn→ ∞ xn = O} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X.
