Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Brodskiy, N."'
We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ and on the fundamental group $\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a topological space $X$ and use it to relate topolo
Externí odkaz:
http://arxiv.org/abs/1206.0071
Autor:
Brodskiy, N., Higes, J.
Given a metric space $X$ of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assouad-Nagata dimension less or equal $n$ if there is a linear dimension fu
Externí odkaz:
http://arxiv.org/abs/0910.2378
Publikováno v:
Topology and its Applications 157 (2010) 2593-2603
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. In this paper we investigate when these covering maps a
Externí odkaz:
http://arxiv.org/abs/0802.4304
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 space. One of characterizations of Peano covering maps is via the uniq
Externí odkaz:
http://arxiv.org/abs/0801.4967
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 covers for uniform spaces generalizing their results for topological gr
Externí odkaz:
http://arxiv.org/abs/0706.3937
Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated. We show that the Assouad-Nagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$ depends on the growth of $G$ as follows: If the growth of $G$ is not bounded by a
Externí odkaz:
http://arxiv.org/abs/math/0611331
Publikováno v:
Colloquium Mathematicum 111 (2008), 149-158
The main results of the paper are: \begin{Prop}\label{GenSvarc-Milnor} A group $G$ acting coarsely on a coarse space $(X,\CC)$ induces a coarse equivalence $g\to g\cdot x_0$ from $G$ to $X$ for any $x_0\in X$. \end{Prop} Theorem: \label{GenGromovThm}
Externí odkaz:
http://arxiv.org/abs/math/0607568
Publikováno v:
Topology and its Applications, 154 (2007), 2729-2740
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unifie
Externí odkaz:
http://arxiv.org/abs/math/0607241
Given a function $f\colon X\to Y$ of metric spaces, its {\it asymptotic dimension} $\asdim(f)$ is the supremum of $\asdim(A)$ such that $A\subset X$ and $\asdim(f(A))=0$. Our main result is \begin{Thm} \label{ThmAInAbstract} $\asdim(X)\leq \asdim(f)+
Externí odkaz:
http://arxiv.org/abs/math/0605416
Publikováno v:
Topology Proceedings 31 (2007)
The famous \v{S}varc-Milnor Lemma says that a group $G$ acting properly and cocompactly via isometries on a length space $X$ is finitely generated and induces a quasi-isometry equivalence $g\to g\cdot x_0$ for any $x_0\in X$. We redefine the concept
Externí odkaz:
http://arxiv.org/abs/math/0603487