Nerve Theorem on a Positive Reach set

03/16/2019

∙

We provide sufficient conditions under which any non-empty intersection of finitely many Euclidean balls intersected with a subset of R^d of positive reach are contractible. Our result allows for an immediate application of the nerve theorem to the problem of recovering the homology of a set based on point cloud data.

READ FULL TEXT

Nerve Theorem on a Positive Reach set

Computable bounds for the reach and r-convexity of subsets of ℝ^d

Optimal Oracles for Point-to-Set Principles

Optimal homotopy reconstruction results à la Niyogi, Smale, and Weinberger

Recent Results on No-Free-Lunch Theorems for Optimization

Theorems of Carathéodory, Helly, and Tverberg without dimension

A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions

Coding information into all infinite subsets of a dense set

Nerve Theorem on a Positive Reach set

Related Research

Computable bounds for the reach and r-convexity of subsets of ℝ^d

Optimal Oracles for Point-to-Set Principles

Optimal homotopy reconstruction results à la Niyogi, Smale, and Weinberger

Recent Results on No-Free-Lunch Theorems for Optimization

Theorems of Carathéodory, Helly, and Tverberg without dimension

A Generalization of the Borkar-Meyn Theorem for Stochastic Recursive Inclusions

Coding information into all infinite subsets of a dense set