The aim of this paper is to show how the homeomorphism and homotopy types of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the space. This recovering allows us to propose an alternative way to construct persistence modules from a point cloud.

中文翻译：

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通过有限逼近和逆持久性重建紧致

本文的目的是说明如何通过空间有限逼近的逆序列的逆极限来构造紧度量空间的同胚和同伦类型。这种恢复使我们可以提出一种从点云构造持久性模块的替代方法。