PreprintarXiv licencearXiv
From samples to shape: a finite approach to topological invariants
Abstract
Given a metric space Y and a compact subspace X, we present a method for constructing an inverse sequence of finite topological spaces by sampling points from neighborhoods of X in Y. We show that these inverse sequences can be employed to define shape theory and to approximate shape invariants, such as Čech homology groups.
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BibTeX
@misc{chocano2026from,
title = {{From samples to shape: a finite approach to topological invariants}},
author = {Pedro J. Chocano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34328},
eprint = {2609.34328},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34328},
}
RIS
TY - UNPB
TI - From samples to shape: a finite approach to topological invariants
AU - Pedro J. Chocano
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34328
UR - https://arxiv.org/abs/2609.34328
AB - Given a metric space Y and a compact subspace X, we present a method for constructing an inverse sequence of finite topological spaces by sampling points from neighborhoods of X in Y. We show that these inverse sequences can be employed to define shape theory and to approximate shape invariants, such as Čech homology groups.
ER -