Notes on (SSP) sets

TL;DR

This paper extends Sampaio's result on bi-Lipschitz homeomorphic tangent cones from subanalytic sets to a broader class called (SSP) sets, showing the method's wider applicability.

Contribution

It demonstrates that Sampaio's method applies to (SSP) sets, establishing a characteristic property for this larger class of sets.

Findings

Sampaio's method extends to (SSP) sets

Bi-Lipschitz homeomorphic (SSP) sets have homeomorphic tangent cones

The result characterizes (SSP) sets via tangent cones

Abstract

Sampaio recently showed that bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones. The purpose of this note is to show that Sampaio's method works as well for (SSP) sets, that is, the above result is characteristic for (SSP) sets, a much wider class.