PreprintCC BY 4.0arXiv
Persistence diagrams of finite topological spaces
Abstract
In this paper, we apply persistent homology to study finite topological spaces by associating persistence diagrams with their elements through the furtherness function. This approach enables us to classify elements according to their topological evolution within the space. We further establish a bottleneck stability theorem showing that the bottleneck distance between the persistence diagrams associated with two elements is bounded above by their mutual furtherness.
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BibTeX
@misc{badra2026persistence,
title = {{Persistence diagrams of finite topological spaces}},
author = {Akhilesh Badra and Hemant Kumar Singh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16386},
eprint = {2610.16386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Persistence diagrams of finite topological spaces
AU - Akhilesh Badra
AU - Hemant Kumar Singh
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16386
UR - https://arxiv.org/abs/2610.16386
AB - In this paper, we apply persistent homology to study finite topological spaces by associating persistence diagrams with their elements through the furtherness function. This approach enables us to classify elements according to their topological evolution within the space. We further establish a bottleneck stability theorem showing that the bottleneck distance between the persistence diagrams associated with two elements is bounded above by their mutual furtherness.
ER -