从样本中确定未知空间的同源性

IF 0.5 Q3 MATHEMATICS European Journal of Mathematics Pub Date : 2023-10-03 DOI:10.1007/s40879-023-00683-4

Morten Brun, Belén García Pascual, Lars M. Salbu

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引用次数: 0

摘要

欧几里得空间的未知子空间的同调性可以由子空间中点样本的内征Čech复形确定，而不需要参考周围的欧几里得空间。更准确地说，给出欧几里得空间的一个子空间X和X上的一个点的样本a，给出X的同构于某一内禀Čech复形的持久同构群的条件。

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Determining homology of an unknown space from a sample

Abstract The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X , we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.

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来源期刊

European Journal of Mathematics MATHEMATICS-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： The European Journal of Mathematics (EJM) is an international journal that publishes research papers in all fields of mathematics. It also publishes research-survey papers intended to provide nonspecialists with insight into topics of current research in different areas of mathematics. The journal invites authors from all over the world. All contributions are required to meet high standards of quality and originality. EJM has an international editorial board. Coverage in EJM will include: - Algebra - Complex Analysis - Differential Equations - Discrete Mathematics - Functional Analysis - Geometry and Topology - Mathematical Logic and Foundations - Number Theory - Numerical Analysis and Optimization - Probability and Statistics - Real Analysis.