Subcontinua of the Higson corona
Subcontinua of the Higson corona
复制标题
希格森日冕的亚连续面
DOI：
10.1016/s0166-8641(97)00009-6
复制
发表时间：
1997
影响因子：
0.6
通讯作者：
J. Keesling
中科院分区：
文献类型：
--
作者：
J. Keesling
设X是具有适当度量d的局部紧可分度量空间。设X的Higson紧化为X的Higson紧化，记X的冠为νdX.本文的主要结果是：若A是νdX的σ-紧子集，则A在νdX中的闭包等价于A的Stone-Čech紧化。这应该与众所周知的事实相比较，如果X是局部紧的和σ-紧的，并且A是βXβX的Lindelöf子集，则A在βXβX中的闭包等价于βA。
Let X be a locally compact separable metric space with proper metric d. Let X ̄ddenote the Higson compactification of X and let νdX denote the corona of X. The main result of this paper is that if A is a σ-compact subset of νdX, then the closure of A in νdX is equivalent to the Stone-Čech compactification of A. This should be compared with the well known fact that, if X is locally compact and σ-compact and A is a Lindelöf subset of βXβX, then the closure of A in βXβX is equivalent to βA.