Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904257 | Topology and its Applications | 2017 | 13 Pages |
Abstract
Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:XâY induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:XâY is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)â¤asdim(X)+nâ1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Kyle Austin, Žiga Virk,