2 citations · 2 across the 6 of their papers we have counts for
6 papers
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…
Embeddings to Rectilinear Space and Gromov-Hausdorff Distances
A. O. Ivanov, A. A. Tuzhilin
We show that the problem whether a given finite metric space can be embedded into -dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance b…
Metric Space Recognition by Gromov-Hausdorff Distances to Simplexes
A. O. Ivanov, E. S. Lychagina, A. A. Tuzhilin
In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance…
Gromov-Hausdorff Geometry of Metric Trees
A. O. Ivanov, I. N. Mikhailov, A. A. Tuzhilin
In this paper, we study metric trees, without any finiteness restrictions. For subsets of such trees, a condition that guarantees that the Hausdorff and Gromov--Hausdorff distances…
When the Gromov-Hausdorff distance between finite-dimensional space and its subset is finite?
I. N. Mikhailov, A. A. Tuzhilin
In this paper we prove that the Gromov--Hausdorff distance between and its subset is finite if and only if is an -net in for some…
Solution to Generalized Borsuk Problem in Terms of the Gromov-Hausdorff Distances to Simplexes
Alexander Ivanov, Alexei Tuzhilin
In the present paper the following Generalized Borsuk Problem is studied: Can a given bounded metric space be partitioned into a given number (probably an infinite one) of…