Simultaneous metrizability of coarse spaces

Wright, Nick

doi:10.1090/S0002-9939-2011-10805-0

Simultaneous metrizability of coarse spaces
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Proc. Amer. Math. Soc. 139 (2011), 3271-3278 Request permission

Abstract:

A metric space can be naturally endowed with both a topology and a coarse structure. We examine the converse to this. Given a topology and a coarse structure we give necessary and sufficient conditions for the existence of a metric giving rise to both of these. We conclude with an application to the construction of the coarse assembly map.

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