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arXiv · 2210.00535

Convergence in the space of compact labeled metric spaces

Reijo Jaakkola·Antti Kykkänen
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Abstract

A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff distance, an extension of the classical Gromov-Hausdorff distance, which measures how close two labeled metric spaces are. We provide a toolbox of results characterizing convergence in the labeled Gromov-Hausdorff distance. We obtain a completeness result for the space of labeled metric spaces and precompactness characterizations for subsets of the space. The results are applied to travel time inverse problems in a labeled metric space context.

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Reijo Jaakkola, Antti Kykkänen. 2022-10-02. Convergence in the space of compact labeled metric spaces. https://arxiv.org/abs/2210.00535

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