Geodesic
Noncompactness of segments in the Gromov–Hausdorff space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2021), pp. 3-8 
O. B. Borisova. Noncompactness of segments in the Gromov–Hausdorff space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2021), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2021_5_a0/
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     title = {Noncompactness of segments in the {Gromov{\textendash}Hausdorff} space},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study properties of segments in the Gromov–Hausdorff metric space. A segment is a subset of a metric space consisting of points lying between two given points. We prove that any segment in the Gromov–Hausdorff space with endpoints being non-isometric compact metric spaces contains an element that is a compact metric space with at least one isolated point. Using this theorem and Gromov's precompactness criterion, we prove that any nondegenerate segment in the Gromov–Hausdorff space is not a compact set.

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