33 citations · 687 across the 231 of their papers we have counts for
8 papers · 1 filter
Metric characterizations of some subsets of the real line
Iryna Banakh, Taras Banakh, Maria Kolinko +1
A metric space is called a if every 3-element subset of can be written as for some points such that . By a cla…
Embedding fractals in Banach, Hilbert or Euclidean spaces
Taras Banakh, Magdalena Nowak, Filip Strobin
By a metric fractal we understand a compact metric space endowed with a finite family of contracting self-maps of such that . I…
Coarse classification of abelian groups and amenable shift-homogeneous metric spaces
Taras Banakh, Matija Cencelj, Dušan Repovš +1
In this paper we classify countable locally finite-by-abelian groups up to coarse isomorphism. This classification is derived from a coarse classification of amenable shift-homogen…
Asymptotic dimension and small subsets in locally compact topological groups
Taras Banakh, Ostap Chervak, Nadya Lyaskovska
We prove that for a coarse space the ideal of small subsets of coincides with the ideal of subsets of asymptotic dimension …
A coarse characterization of the Baire macro-space
Taras Banakh, Ihor Zarichnyi
We prove that each coarsely homogenous separable metric space is coarsely equivalent to one of the spaces: the sigleton, the Cantor macro-cube or the Baire macro-space. This cl…
Characterizing the Cantor bi-cube in asymptotic categories
Taras Banakh, Ihor Zarichnyi
We present the characterization of metric spaces that are micro-, macro- or bi-uniformly equivalent to the extended Cantor set $\{\sum_{i=-n}^\infty\frac{2x_i}{3^i}:n\in\IN ,\;(x_i…