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arXiv · 2410.05617

An axiomatic treatment of Persistent Homology

Sergio Tsuyoshi Ura·Marco Contessoto·Alice Kimie Miwa Libardi
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Abstract

We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of axioms.

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Sergio Tsuyoshi Ura, Marco Contessoto, Alice Kimie Miwa Libardi. 2024-10-08. An axiomatic treatment of Persistent Homology. https://arxiv.org/abs/2410.05617

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