CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 54C20 ( Extension of maps )

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM Online first

Mine, Kotaro; Yamashita, Atsushi
Metric compactifications and coarse structures
Let $\mathbf{TB}$ be the category of totally bounded, locally compact metric spaces with the $C_0$ coarse structures. We show that if $X$ and $Y$ are in $\mathbf{TB}$ then $X$ and $Y$ are coarsely equivalent if and only if their Higson coronas are homeomorphic. In fact, the Higson corona functor gives an equivalence of categories $\mathbf{TB}\to\mathbf{K}$, where $\mathbf{K}$ is the category of compact metrizable spaces. We use this fact to show that the continuously controlled coarse structure on a locally compact space $X$ induced by some metrizable compactification $\tilde{X}$ is determined only by the topology of the remainder $\tilde{X}\setminus X$.

Keywords:coarse geometry, Higson corona, continuously controlled coarse structure, uniform continuity, boundary at infinity
Categories:18B30, 51F99, 53C23, 54C20

© Canadian Mathematical Society, 2015 : https://cms.math.ca/