Approximations of Stone–Cech compactifications by Higson compactifications
Volume 88 / 2001
Colloquium Mathematicum 88 (2001), 75-92
MSC: Primary 54D35, 54D40.
DOI: 10.4064/cm88-1-7
Abstract
The Higson compactification ${\hskip 2.2pt\overline {\hskip -2.2pt X\hskip -.7pt}\hskip .7pt}^d$ of a non-compact proper metric space $(X,d)$ is rarely equivalent to the Stone–{\accent 20 C}ech compactification $\beta X$. We give a characterization of such spaces. Also, we show that for each non-compact locally compact separable metric space, $\beta X$ is equivalent to $\lim\limits_{\longleftarrow}\{{\hskip2.2pt\overline{\hskip-2.2pt X\hskip-.7pt}\hskip.7pt}^d:d$ 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.
