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Simultaneous metrizability of coarse spaces


Author: Nick Wright
Journal: Proc. Amer. Math. Soc. 139 (2011), 3271-3278
MSC (2010): Primary 46L85, 51F99
Published electronically: April 6, 2011
MathSciNet review: 2811282
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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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Additional Information

Nick Wright
Affiliation: Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ, United Kingdom
Email: wright@soton.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2011-10805-0
Keywords: Coarse geometry, metrizability, assembly map
Received by editor(s): September 22, 2009
Received by editor(s) in revised form: August 13, 2010
Published electronically: April 6, 2011
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.