A natural compactification of the Gromov-Hausdorff space
Hiroki Nakajima, Takashi Shioya
TL;DR
This paper introduces a pseudometric to compactify the Gromov-Hausdorff space, providing a natural extension compatible with ultralimits, advancing the understanding of metric space convergence.
Contribution
It presents a novel pseudometric that yields a natural compactification of the Gromov-Hausdorff space, enhancing the theoretical framework of metric space analysis.
Findings
Defined a new pseudometric on isometry classes of metric spaces
Established a natural compactification compatible with ultralimits
Improved the theoretical understanding of Gromov-Hausdorff space convergence
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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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Banach Space Theory