How many miles to βX? : d miles, or just one foot
How many miles to βX? : d miles, or just one foot
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βX 是多少英里：d 英里，或者只是一英尺？
DOI：
10.1016/j.topol.2005.07.016
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发表时间：
2006
影响因子：
0.6
通讯作者：
Y. Yoshinobu
中科院分区：
文献类型：
--
作者：
M. Kada;Kazuo Tomoyasu;Y. Yoshinobu
已知可度量空间X的Stone -Čech紧化βX可近似为X上所有相容度量的Smirnov紧化集合，如果我们将自己限制在局部紧化可度量空间，则对Higson紧化成立。我们研究了X上兼容度量集合D的最小基性，使得βX对D上的所有度量都是Smirnov紧化或Higson紧化。我们证明了它是局部紧化可分可度量空间的支配数或1。
It is known that the Stone–Čech compactification βX of a metrizable space X is approximated by the collection of Smirnov compactifications of X for all compatible metrics on X. If we confine ourselves to locally compact separable metrizable spaces, the corresponding statement holds for Higson compactifications. We investigate the smallest cardinality of a set D of compatible metrics on X such that βX is approximated by Smirnov or Higson compactifications for all metrics in D. We prove that it is either the dominating number or 1 for a locally compact separable metrizable space.