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math.GN2022
Gromov-Hausdorff Distance and Borsuk Number
Alexander Ivanov, Alexey Tuzhilin
The aim of this paper is to demonstrate relations between Gromov-Hausdorff distance properties and the Borsuk Conjecture. The Borsuk number of a given bounded metric space is t…
math.MG2022
Calculating Gromov-Hausdorff Distance by means of Borsuk Number
Alexander O. Ivanov, Alexey A. Tuzhilin
The purpose of this article is to demonstrate the connection between the properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The Borsuk number of a given bounde…
math.MG2022
Isometric Embeddings of Bounded Metric Spaces into the Gromov-Hausdorff Class
Alexander O. Ivanov, Alexey A. Tuzhilin
It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of th…