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...
| Authors: | , , |
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| 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 |
| 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. |
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