15 citations · 37 across the 7 of their papers we have counts for
7 papers
Topological and uniform structures on universal covering spaces
N. Brodskiy, J. Dydak, B. Labuz +1
We discuss various uniform structures and topologies on the universal covering space and on the fundamental group . We introduce a canonical uniform stru…
Assouad-Nagata dimension of tree-graded spaces
N. Brodskiy, J. Higes
Given a metric space of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assoua…
Group Actions and Covering Maps in the Uniform Category
N. Brodskiy, J. Dydak, B. Labuz +1
In Rips Complexes and Covers in the Uniform Category (arXiv:0706.3937) we define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform…
Covering maps for locally path-connected spaces
N. Brodskiy, J. Dydak, B. Labuz +1
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological…
Rips complexes and covers in the uniform category
N. Brodskiy, J. Dydak, B. Labuz +1
James \cite{Jam} introduced uniform covering maps as an analog of covering maps in the topological category. Subsequently Berestovskii and Plaut \cite{BP3} introduced a theory of c…
Compression of uniform embeddings into Hilbert space
N. Brodskiy, D. Sonkin
If one tries to embed a metric space uniformly in Hilbert space, how close to quasi-isometric could the embedding be? We answer this question for finite dimensional CAT(0) cube com…