Approximations of Stone-Cech compactifications by Higson compactifications
Approximations of Stone-Cech compactifications by Higson compactifications
复制标题
通过 Higson 紧化近似 Stone-Cech 紧化
DOI：
10.4064/cm88-1-7
复制
发表时间：
2001
影响因子：
0.4
通讯作者：
Kazuo Tomoyasu
中科院分区：
文献类型：
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作者：
K. Kawamura;Kazuo Tomoyasu
非紧真度量空间 (X, d) 的 Higson 紧化 X d 很少等于 Stone-Čech 紧化 βX。我们给出了此类空间的特征。此外，我们还证明，对于每个非紧局部紧可分离度量空间，βX 等价于 lim ←−{X d ： d 是 X 上的适当度量，与 X} 的拓扑兼容。通过一些例子和应用来说明上述类型的近似方法。
The Higson compactification X d of a non-compact proper metric space (X, d) is rarely equivalent to the Stone–Čech compactification βX. We give a characterization of such spaces. Also, we show that for each non-compact locally compact separable metric space, βX is equivalent to lim ←−{X d : d is a proper metric on X which is compatible with the topology of X}. The approximation method of the above type is illustrated by some examples and applications.