\(C_0\) coarse structures on uniform spaces (Q2786846)

Coarse structures capture the asymptotic behaviour of spaces. They usually arise from a metric (bounded coarse structure) or from a compactification (topological coarse structure) of a given topological space. Another approach introduced by Wright is to define the \(C_0\) coarse structure of a locally compact metric space. It turns out that each of the mentioned coarse structures may be obtained as an appropriate topological coarse structure.NEWLINENEWLINEIn this paper the authors generalize the definition of the \(C_0\) coarse structure to uniform spaces. The main result states that every topological coarse structure of a locally compact Hausdorff space is the \(C_0\) coarse structure associated to some uniform structure compatible with its topology.