Vietoris--Rips Contractibility for Dense Subsets of Finite-Dimensional Normed Spaces

Qingsong Wang, Ling Zhou

Let $Y$ be a $\delta$-dense subset of a finite-dimensional normed space $X$, so every point of $X$ is at distance at most $\delta$ from some point of $Y$. We prove that the open Vietoris--Ri…