Geometry of Geometric Data Set I
Metric Geometry
2026-03-25 v1
Abstract
Hanika, Schneider, and Stumme introduced geometric data set as a generalization of metric measure space for the computation of the observable diameter, and extended the observable distance between metric measure spaces to that between geometric data sets. In this paper, we begin by proving the non-separability of the observable distance between geometric data sets. We then extend the box distance between mm-spaces to that between geometric data sets and prove its completeness and non-separability.
Keywords
Cite
@article{arxiv.2603.23316,
title = {Geometry of Geometric Data Set I},
author = {Shigeaki Yokota},
journal= {arXiv preprint arXiv:2603.23316},
year = {2026}
}