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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Kalantari, S. A Concept for Resemblance in Large Scale Geometry. Results Math 79, 6 (2024). https://doi.org/10.1007/s00025-023-02029-8
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DOI: https://doi.org/10.1007/s00025-023-02029-8