Abstract:This paper studies coarse compactifications and their boundary. We introduce two alternative descriptions to Roe's original definition of coarse compactification. One approach uses bounded functions on X that can be extended to the boundary. They satisfy the Higson property exactly when the compactification is coarse. The other approach defines a relation on subsets of X which tells when two subsets closure meet on the boundary. A set of axioms characterizes when this relation defines a coarse compactification… Show more
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