Generalisations of coarse spaces

@article{Zava2019GeneralisationsOC,
  title={Generalisations of coarse spaces},
  author={Nicol{\`o} Zava},
  journal={Topology and its Applications},
  year={2019}
}
  • N. Zava
  • Published 28 May 2018
  • Mathematics
  • Topology and its Applications
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a large-scale counterpart of uniformities. In the literature, there are very important generalisations of uniform spaces, such as semi-uniform and quasi-uniform spaces. In this paper, we introduce and start to study their large-scale counterparts, which generalise coarse spaces: semi-coarse spaces and quasi-coarse spaces. 
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References

SHOWING 1-10 OF 30 REFERENCES
An alternative definition of coarse structures
Abstract Roe [J. Roe, Lectures on Coarse Geometry, University Lecture Series, vol. 31, Amer. Math. Soc., Providence, RI, 2003] introduced coarse structures for arbitrary sets X by considering subsetsExpand
Coarse structures on groups
Abstract We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. WeExpand
Some categorical aspects of coarse spaces and balleans
Abstract Coarse spaces [26] and balleans [23] are known to be equivalent constructions ( [25] ). The main subject of this paper is the category, Coarse , having as objects these structures, and itsExpand
Lectures on coarse geometry
Metric spaces Coarse spaces Growth and amenability Translation algebras Coarse algebraic topology Coarse negative curvature Limits of metric spaces Rigidity Asymptotic dimension Groupoids and coarseExpand
Uniform Spaces, I
Publisher Summary Uniform spaces can be defined in various equivalent ways. Every uniform space carries a natural topology; it is defined using neighborhood bases. A uniformly continuous map is alsoExpand
Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics
Preface. Introduction. 1. Preliminaries on Subobjects, Images, and Inverse Images. 2. Basic Properties of Closure Operators. 3. Examples of Closure Operators. 4. Operations on Closure Operators. 5.Expand
Balleans, hyperballeans and ideals
A ballean B (or a coarse structure) on a set X is a family of subsets of X called balls (or entourages of the diagonal in X × X) dened in such a way that B can be considered as the asymptoticExpand
Cover quasi-uniformities in frames
Abstract Quasi-uniformities (not necessarily symmetric uniformities) are usually studied via entourages (special neighbourhoods of the diagonal in X × X ) where one can simply forget about theExpand
TOPICS IN GEOMETRIC GROUP THEORY
We present a brief overview of methods and results in geometric group theory, with the goal of introducing the reader to both topological and metric perspectives. Prerequisites are kept to a minimum:Expand
On hyperballeans of bounded geometry
A ballean (or coarse structure) is a set endowed with some family of subsets, the balls, in such a way that balleans with corresponding morphisms can be considered as asymptotic counterparts ofExpand
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