I. N. Mikhailov

collaborators

3 papers

math.MG2026

Contractibility of the space of $ε$ -nets in $R$

Ivan N. Mikhailov

In this note, we show that the space of all $ε$ -nets in the real line $R$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is…

math.MG2025

New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line

Ivan N. Mikhailov

In the paper we prove that, for arbitrary unbounded subset $A \subset R$ and an arbitrary bounded metric space~ $X$ , a curve $A \times_{ℓ^{1}} (tX)$ , $t \in [0, \infty)$ is a geodesic…

math.MG2025

Ultrametric spaces and clouds

I. N. Mikhailov

In ``Characterization, stability and convergence of hierarchical clustering methods'' by G. E. Carlsson, F. Memoli, the natural way to construct an ultrametric space from a given m…

Contractibility of the space of ε-nets in R

New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line

Ultrametric spaces and clouds

Contractibility of the space of $ε$ -nets in $R$