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Polyhedral expansions of compacta associated to finite approximations

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This paper introduces some inverse sequences of different polyhedra all based on finite approximations of a compact metric space so they can be used to capture the shape type of the original space. It is shown that they are HPol-expansions, proving the so-called general principle. We use these sequences to compute explicitly some inverse persistent homology groups of a space and measure its errors in the approximation process.

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Acknowledgements

The author wishes to thank the valuable help, comments and support from his thesis advisor M.A. Morón for the results obtained in this article.

Funding

This work has been partially supported by the research project PGC2018-098321-B-I00 (MICINN). The author has been also supported by the FPI Grant BES-2010-033740 of the project MTM2009-07030 (MICINN).

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  1. Departmento de Matemática Aplicada y Estadística, Universidad San Pablo-CEU, CEU Universities, Julián Romea 23, 28003, Madrid, Madrid, Spain

    Diego Mondéjar

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Mondéjar, D. Polyhedral expansions of compacta associated to finite approximations. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 99 (2022). https://doi.org/10.1007/s13398-022-01236-2

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