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Approximations of Stone-Čech compactifications by Higson compactifications. (English) Zbl 1001.54022
Summary: The Higson compactification \({\overline X}^d\) of a non-compact proper metric space \((X,d)\) is rarely equivalent to the Stone-Čech 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 \(\varprojlim{\overline X}^d\): \(d\) 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.

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D40 Remainders in general topology
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