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arXiv · 2202.05915

Collapsing Maps and Quasi-Isometries

Josh Thompson·Davin Hemmila
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Abstract

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 $\psi: X \longrightarrow Y$ 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.

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Josh Thompson, Davin Hemmila. 2022-02-11. Collapsing Maps and Quasi-Isometries. https://arxiv.org/abs/2202.05915

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