PreprintCC BY-NC-ND 4.0arXiv
Yet another approach to measuring distance in some hyperspaces
Abstract
In this article, we define a new partial distance on hyperspaces consisting of closed balls, which is a partial metric in the sense of Matthews. We prove that these partial metric spaces are complete if and only if the metric spaces from which the corresponding ball spaces arise are complete. Finally, we compare the topology induced by the new partial distance with that induced by the classical Hausdorff distance.
Related
- Some results on the distance spectral radius and edge-disjoint spanning trees of graphs
- Calibers of canonical hyperconnected spaces and their Vietoris hyperspaces
- Super calibers in topological spaces and topological hyperspaces
- Surjective Hausdorff Isometries of Hyperspaces of Bounded Closed Convex Sets
- Extending graph metrics to hyperspaces of vertex sets: optimization and reinforcement learning applications
BibTeX
@misc{bugajewski2026another,
title = {{Yet another approach to measuring distance in some hyperspaces}},
author = {Dariusz Bugajewski and Piotr Maćkowiak},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00249},
eprint = {2611.00249},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00249},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Yet another approach to measuring distance in some hyperspaces
AU - Dariusz Bugajewski
AU - Piotr Maćkowiak
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00249
UR - https://arxiv.org/abs/2611.00249
AB - In this article, we define a new partial distance on hyperspaces consisting of closed balls, which is a partial metric in the sense of Matthews. We prove that these partial metric spaces are complete if and only if the metric spaces from which the corresponding ball spaces arise are complete. Finally, we compare the topology induced by the new partial distance with that induced by the classical Hausdorff distance.
ER -