Abstract
In this paper, we introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Using it, we obtain a natural compactification of the Gromov–Hausdorff space, which is compatible with ultralimit.
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Acknowledgements
The authors would like to thank the referee for carefully reading the manuscript and for his/her useful comments. We would also like to thank Shun Oshima for his comment.
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This work was supported by JSPS KAKENHI Grant Number 19K03459 and 19J10866.
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Nakajima, H., Shioya, T. A natural compactification of the Gromov–Hausdorff space. Geom Dedicata 218, 10 (2024). https://doi.org/10.1007/s10711-023-00852-5
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DOI: https://doi.org/10.1007/s10711-023-00852-5