Reconstruction of compacta by finite approximations and inverse persistence

Reconstruction of compacta by finite approximations and inverse persistence

The aim of this paper is to show how the homeomorphism and homotopy types of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the space. This recovering allows us to propose an alternative way to construct persistence modules from a p...

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Veröffentlicht in:Revista matemática complutense 2021-05, Vol.34 (2), p.559-584
Hauptverfasser: Mondéjar Ruiz, Diego, Morón, Manuel A.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Approximation
Geometry
Mathematics
Mathematics and Statistics
Metric space
Topology
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Zusammenfassung:The aim of this paper is to show how the homeomorphism and homotopy types of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the space. This recovering allows us to propose an alternative way to construct persistence modules from a point cloud.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-020-00356-w