2022/02/11 by Thompson, Josh, Hemmila, Davin
#FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2202.05915
We introduce a generalization of the b-metric we call a (b,c)-metric. We show that if X is a (b,c)-metric space and ψ: X \longrightarrow Y is a quasi-isometry then Y is (b,c)-metrizable. We also define a particular kind of collapsing map that can be applied to an arbitrary (b,c)-metric space. We define a distance function on the image of this collapsing map and with this prove that the collapsing map is a quasi-isometry.