一类非紧度量空间上的连续函数空间（英文）  

Spaces of Continuous Maps on a Class of Noncompact Metric Spaces

作　　者：吴拿达[1] 杨忠强[2] 

机构地区：[1]韩山师范学院数学与应用数学系,潮州广东521041 [2]汕头大学数学系,汕头广东515063

出　　处：《数学进展》2013年第4期535-541,共7页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.10971125);the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20094402110001);Hanshan Normal University Start-up Project for Ph.D.(No.QD20091202)

摘　　要：对一个度量空间(X,ρ),设↓C(X)是从X到I=[0,1]的连续函数下方图形全体之集赋予由度量空间X×I上的Hausdorff度量诱导出的拓扑.本文证明了下面的结果:如果(X,ρ)是一个非紧的、局部紧的、可分的、完全有界的度量空间,则↓C(X)同胚于c_0当且仅当X上的孤立点全体之集在X中不稠密,这里c_0={(xn)n∈N∈[-1,1]ω:sup|x+n|<1且lim_(n→+∞)x_n=0}.特别地,对赋予通常度量的开区间(0,1),↓C((0,1))同胚于c_0.Abstract： For a metric space （X, p）, let ↓C（X） be the family of hypographs of all continuous maps from X to I= [0,1] endowed with the topology induced by the Hausdorff metric of the metric space X × I. In the present paper, the following result is proved： if （X, p） is a noncompact, locally compact, totally bounded, separable metric space, then ↓C（X） is home- omorphic to co if and only if the set of all isolated points of X is not dense in X, where co =c0={（xn）n∈N∈[-1,1]^ω： sup[xn] 〈 1 and limn-＋∞ xn = 0}. Specially, for the open interval （0, 1） with the usual metric, ↓C（（0, 1）） is homeomorphic to co.

关 键 词：连续函数 非紧空间 Hausdorff拓扑 吸收子 

分 类 号：O189.11[理学—数学]