Approximations of Stone–Cech compactifications by Higson compactifications

Kazuhiro Kawamura ¹   ; Kazuo Tomoyasu ²

¹ Institute of Mathematics University of Tsukuba Tsukuba-shi Ibaraki 305-8571, Japan
² Miyakonojo National College of Technology Miyakonojo-shi Miyazaki 885-8567, Japan

Colloquium Mathematicum, Tome 88 (2001) no. 1, pp. 75-92

Résumé

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.

Détail

DOI : 10.4064/cm88-1-7

Keywords: higson compactification hskip overline hskip hskip hskip non compact proper metric space rarely equivalent stone accent ech compactification beta characterization spaces each non compact locally compact separable metric space beta equivalent lim limits longleftarrow hskip overline hskip hskip hskip proper metric which compatible topology approximation method above type illustrated examples applications