2021/03/28 by Igor Protasov, Protasov, Igor
Mathematics · #FOS: Mathematics #General Topology (math.GN) #math.GN
paper · pdf · doi:10.48550/arxiv.2104.10654
coarse structure, 2-selector of a graph, linear order compatible with a coarse structure. arXiv admin note: text overlap with arXiv:2102.03790, arXiv:2102.02053
arxiv created 2021/09/07 · arxiv updated 2021/09/08
We consider a connected graph Γ as a coarse space and prove that Γ admits a 2-selector if and only if Γ is either bounded or coarsely equivalent to ℕ or ℤ. We apply this result to geodesic metric spaces admitting linear orders compatible with coarse structures.