Generalisations of coarse spaces

  title={Generalisations of coarse spaces},
  author={Nicol{\`o} Zava},
  journal={Topology and its Applications},
  • 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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