Strong topology on the set of persistence diagrams
General Topology
2020-05-22 v1 Metric Geometry
Abstract
We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. Also, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.
Keywords
Cite
@article{arxiv.2005.10773,
title = {Strong topology on the set of persistence diagrams},
author = {Volodymyr Kiosak and Aleksandr Savchenko and Mykhailo Zarichnyi},
journal= {arXiv preprint arXiv:2005.10773},
year = {2020}
}
Comments
6 pages