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math.MG2026
Mazur-Ulam Theorem With Gromov-Hausdorff Distance
S. A. Bogaty, A. A. Tuzhilin
It is shown that two Banach spaces are linearly isometric if and only if the Gromov--Hausdorff distance between them is finite, in particular, zero. The proof is compilative and re…
math.MG2025
Fundamentals of Theory of Continuous Gromov--Hausdorff distance
Semeon A. Bogaty, Alexey A. Tuzhilin
The Gromov--Hausdorff distance (hereinafter referred to as the GH-distance) is a measure of non-isometricity of metric spaces. In this paper, we study a modification of this distan…
math.MG2021★ 8 cited
Gromov-Hausdorff class: its completeness and cloud geometry
Semeon A. Bogaty, Alexey A. Tuzhilin
The paper is devoted to the study of the Gromov-Hausdorff proper class, consisting of all metric spaces considered up to isometry. In this class, a generalized Gromov-Hausdorff pse…