Finite presentation of finitely determined modules

TL;DR

This paper demonstrates that finitely determined modules in topological data analysis can be made finitely presented by adding infinitary points, providing a new understanding of their structure.

Contribution

It introduces a method to convert finitely determined modules into finitely presented modules through the addition of infinitary points.

Findings

Finitely determined modules become finitely presented with infinitary points.

Provides a new perspective on the structure of modules in topological data analysis.

Enhances the theoretical framework for tameness in persistence modules.

Abstract

In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely presented.