English

Some counterexamples in abstract coarse geometry

General Topology 2019-04-26 v1

Abstract

We construct an example of a coarse proximity space that is not induced by any coarse structure. We then show how to "stitch" two coarse proximity spaces with homeomorphic boundaries into one coarse proximity space. Finally, we construct a coarse proximity space that is not induced by any asymptotic resemblance structure.

Cite

@article{arxiv.1904.11408,
  title  = {Some counterexamples in abstract coarse geometry},
  author = {Pawel Grzegrzolka and Jeremy Siegert},
  journal= {arXiv preprint arXiv:1904.11408},
  year   = {2019}
}

Comments

7 pages

R2 v1 2026-06-23T08:49:32.082Z