The Hyperspace of the Regions below Continuous Maps with the Fell Topology

作     者：Zhong Qiang YANG Bao Can ZHANG 

作者机构：Department of MathematicsShantou UniversityShantou 515063P.R.China Chengyi CollegeJimei UniversityXiamen 361021P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第1期

页      面：57-66页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070104[理学-应用数学] 081201[工学-计算机系统结构] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by National Natural Science Foundation of China (Grant No.10971125) 

主　　题：Fell topology hyperspace upper semi-continuous Hilbert cube 

摘      要：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.