Reconstruction of compacta by finite approximations and Inverse Persistence

TL;DR

This paper demonstrates how the homotopy type of compact metric spaces can be reconstructed through inverse limits of finite approximations, introducing inverse persistence as a novel persistence method.

Contribution

It introduces a new approach to reconstructing compacta using inverse limits and defines inverse persistence as a new persistence process.

Findings

Homotopy type can be reconstructed from finite approximations.

Inverse persistence is established as a new persistence framework.

Provides a method for analyzing compact metric spaces.

Abstract

The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.