Asymptotic Resemblance

Sh. Kalantari; B. Honari

doi:10.1216/rmj-2016-46-4-1231

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arXiv · 1310.6313

Asymptotic Resemblance

Sh. Kalantari·B. Honari

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Abstract

Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a large scale structure on it. We use our notion of asymptotic resemblance to generalize some basic concepts of coarse geometry. We introduce a large scale compactification which in special cases agrees with Higson compactification. At the end we show that how the asymptotic dimension of a metric space can be generalized to a set equipped with an asymptotic resemblance relation.

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BibTeX RIS

Sh. Kalantari, B. Honari. 2013-10-23. Asymptotic Resemblance. https://doi.org/10.1216/rmj-2016-46-4-1231

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