S. Bogatyi

activity

20022026

most citedRoberts' type embeddings and conversion of the transversal Tverberg's theorem

8 citations · 18 across the 9 of their papers we have counts for

collaborators

9 papers

math.MG2026

Gromov-Hausdorff distance and Jung constant of finite-dimensional normed spaces

Henry Adams, Semeon A. Bogatyi, Florian Frick +5

For a finite-dimensional normed space $V$ and a subset $X$ with finite Hausdorff distance from $V$ , we prove that the Gromov--Hausdorff distance between $X$ and $V$ is at least the…

math.GR2016

On Topologies on the Group $(Z_{p})^{N}$

I. K. Babenko, S. A. Bogatyi

It is proved that, on any Abelian group of infinite cardinality $m$ , there exist precisely $2^{2^{m}}$ nonequivalent bounded Hausdorff group topologies. Under the continu…

math.AT2011★ 1 cited

On intersections of closed curves on surfaces

Semeon A. Bogatyi, Elena A. Kudryavtseva, Heiner Zieschang

The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classe…

math.GN2010

Embeddings of finite-dimensional compacta in Euclidean spaces

S. Bogataya, S. Bogatyi, V. Valov

If $g$ is a map from a space $X$ into $R^{m}$ and $q$ is an integer, let $B_{q, d, m} (g)$ be the set of all lines $Π^{d} \subset R^{m}$ such that $∣ g^{- 1} (Π^{d}) ∣ \geq q$ . Let a…

math.GN2010

Special embeddings of finite-dimensional compacta in Euclidean spaces

S. Bogatyi, V. Valov

If $g$ is a map from a space $X$ into $R^{m}$ and $z \neq \in g (X)$ , let $P_{2, 1, m} (g, z)$ be the set of all lines $Π^{1} \subset R^{m}$ containing $z$ such that $|g^{-1}(Π^1)…

math.GR2009★ 4 cited

On topological properties of the formal power series substitution group

I. Babenko, S. Bogatyi

Certain topological properties of the group $\J(\k)$ of all formal one-variable power series with coefficients in a topological unitary ring $\k$ are considered. We show, in partic…