Classical and continuous Gromov-Hausdorff distances
Metric Geometry
2026-03-30 v1
Abstract
Starting from the definition of the Gromov-Hausdorff distance via distortion of correspondences, we add the requirement of semicontinuity of each correspondence and its inverse. It turns out that in the case of lower semicontinuity we obtain the same classical Gromov-Hausdorff distance, while for upper semicontinuity we are able to prove coincidence with the classical one only in cases where the spaces are either totally bounded or boundedly compact.
Keywords
Cite
@article{arxiv.2603.26428,
title = {Classical and continuous Gromov-Hausdorff distances},
author = {K. V. Semenov and A. A. Tuzhilin},
journal= {arXiv preprint arXiv:2603.26428},
year = {2026}
}
Comments
11 pages