Computational approximations of compact metric spaces

Pedro J. Chocano; Manuel A. Morón; Francisco R. Ruiz del Portal

doi:10.1016/j.physd.2022.133168

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arXiv · 2107.11271

Computational approximations of compact metric spaces

Pedro J. Chocano·Manuel A. Morón·Francisco R. Ruiz del Portal

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Abstract

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ 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.

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BibTeX RIS

Pedro J. Chocano, Manuel A. Morón, Francisco R. Ruiz del Portal. 2021-07-23. Computational approximations of compact metric spaces. https://doi.org/10.1016/j.physd.2022.133168

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