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Path Connectedness of Spheres in Gromov-Hausdorff Space

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Abstract

The path connectedness of spheres in Gromov-Hausdorff space is studied. It is proved that (1) each sphere centered at the single point space is path connected; (2) for any compact metric space X there exists a number RX such that each sphere centered at X and whose radius is greater than RX is path connected.

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References

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    R. A. Tsvetnikov

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  1. R. A. Tsvetnikov
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Correspondence to R. A. Tsvetnikov.

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Tsvetnikov, R.A. Path Connectedness of Spheres in Gromov-Hausdorff Space. Moscow Univ. Math. Bull. 74, 70–74 (2019). https://doi.org/10.3103/S0027132219020062

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  • DOI: https://doi.org/10.3103/S0027132219020062

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