A concept for resemblance in large scale geometry
Geometric Topology
2023-01-24 v1 Logic
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.
Cite
@article{arxiv.2301.09092,
title = {A concept for resemblance in large scale geometry},
author = {Shahab Kalantari},
journal= {arXiv preprint arXiv:2301.09092},
year = {2023}
}