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Topological spaces of persistence modules and their properties. (English) Zbl 1423.55012

Summary: Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties.

MSC:

55N99 Homology and cohomology theories in algebraic topology
54D99 Fairly general properties of topological spaces
54E99 Topological spaces with richer structures
18A25 Functor categories, comma categories
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