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arXiv · 1307.3943

Coarse amenability and discreteness

Jerzy Dydak
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Abstract

This paper is devoted to dualization of paracompactness to the coarse category via the concept of $R$-disjointness. Property A of G.Yu can be seen as a coarse variant of amenability via partitions of unity and leads to a dualization of paracompactness via partitions of unity. On the other hand, finite decomposition complexity of G.Yu and straight finite decomposition complexity of Dranishnikov-Zarichnyi employ $R$-disjointness as the main concept. We generalize both concepts to that of countable asymptotic dimension and our main result shows that it is a subclass of of spaces with Property A. In addition, it gives a necessary and sufficient condition for spaces of countable asymptotic dimension to be of finite asymptotic dimension.

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Jerzy Dydak. 2013-07-15. Coarse amenability and discreteness. https://doi.org/10.1017/s1446788715000312

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