Higson compactification and dimension raising Austin, Kyle Virk, Ziga Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y 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:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. 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. Elsevier 2017 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/521 Austin K, Virk Z. Higson compactification and dimension raising. <i>Topology and its Applications</i>. 2017;215:45-57. doi:<a href="https://doi.org/10.1016/j.topol.2016.10.005">10.1016/j.topol.2016.10.005</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.topol.2016.10.005 info:eu-repo/semantics/altIdentifier/issn/0166-8641 info:eu-repo/semantics/altIdentifier/wos/000390501400005 info:eu-repo/semantics/altIdentifier/arxiv/1608.03954 info:eu-repo/semantics/openAccess