A concept for resemblance in large scale geometry

Shahab Kalantari

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arXiv · 2301.09092

A concept for resemblance in large scale geometry

Shahab Kalantari

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Abstract

In this paper, we introduce the notion of large scale resemblance structure as a new large scale structure by axiomatizing the concept of `being alike in large scale' for a family of subsets of a set. We see that in a particular case, large scale resemblances on a set can induce a nearness on it, and as a consequence, we offer a relatively big class of examples to show that `not every near family is contained in a bunch'. Besides, We show how some large scale properties like asymptotic dimension can be generalized to large scale resemblance spaces.

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Shahab Kalantari. 2023-01-22. A concept for resemblance in large scale geometry. https://arxiv.org/abs/2301.09092

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