PreprintCC BY-NC-ND 4.0arXiv
On the Gromov product and its generalization in partial metric spaces
Abstract
The first aim of this article is to extend the notion of the Gromov product to the class of partial metric spaces. A relation between δ-hyperbolicity of a partial metric space and δ-hyperbolicity of metric spaces endowed with the metrics defined via that partial metric is also established. The second one is to analyze the Gromov product in the wide class of metric spaces in which metrics are defined via Chebyshev sets. Midpoint mappings in this class of spaces will be also examined.
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BibTeX
@misc{bugajewski2026gromov,
title = {{On the Gromov product and its generalization in partial metric spaces}},
author = {Dariusz Bugajewski and Kacper Jarosiński},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10059},
eprint = {2609.10059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10059},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the Gromov product and its generalization in partial metric spaces
AU - Dariusz Bugajewski
AU - Kacper Jarosiński
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10059
UR - https://arxiv.org/abs/2609.10059
AB - The first aim of this article is to extend the notion of the Gromov product to the class of partial metric spaces. A relation between δ-hyperbolicity of a partial metric space and δ-hyperbolicity of metric spaces endowed with the metrics defined via that partial metric is also established. The second one is to analyze the Gromov product in the wide class of metric spaces in which metrics are defined via Chebyshev sets. Midpoint mappings in this class of spaces will be also examined.
ER -