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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.

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