Computational approximations of compact metric spaces

Given a compact metric space X, we associate to it an inverse sequence of finite T0 topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of X that is a strong deformation retract. We provide a method to approximate the homology groups of X and other algebraic i...

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Bibliographic Details
Authors: Chocano Feito, Pedro José, Alonso Morón, Manuel, Romero Ruiz Del Portal, Francisco
Format: article
Publication Date:2022
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/72054
Online Access:https://hdl.handle.net/20.500.14352/72054
Access Level:Open access
Keyword:512
515.1
Finite topological spaces
Compact metric spaces
Approximation
Homotopy
Homology groups
Álgebra
Topología
1201 Álgebra
1210 Topología
Description
Summary:Given a compact metric space X, we associate to it an inverse sequence of finite T0 topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of X that is a strong deformation retract. We provide a method to approximate the homology groups of X and other algebraic invariants. Finally, we study computational aspects and the implementation of this method.