Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Badra, Akhilesh, Singh, Hemant Kumar
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G7031224598, G7065057901
OpenAlex ID: W7221807077