{"type":"journal_article","volume":215,"date_updated":"2021-01-12T08:01:21Z","publist_id":"7299","language":[{"iso":"eng"}],"intvolume":"       215","publication_identifier":{"issn":["01668641"]},"title":"Higson compactification and dimension raising","quality_controlled":"1","doi":"10.1016/j.topol.2016.10.005","author":[{"last_name":"Austin","first_name":"Kyle","full_name":"Austin, Kyle"},{"full_name":"Virk, Ziga","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","last_name":"Virk"}],"_id":"521","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"oa_version":"Submitted Version","abstract":[{"text":"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.","lang":"eng"}],"publication":"Topology and its Applications","publication_status":"published","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:46:56Z","month":"01","citation":{"ama":"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>","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” <i>Topology and Its Applications</i>, vol. 215, Elsevier, 2017, pp. 45–57, doi:<a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">10.1016/j.topol.2016.10.005</a>.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” <i>Topology and its Applications</i>, vol. 215. Elsevier, pp. 45–57, 2017.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">https://doi.org/10.1016/j.topol.2016.10.005</a>.","apa":"Austin, K., &#38; Virk, Z. (2017). Higson compactification and dimension raising. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">https://doi.org/10.1016/j.topol.2016.10.005</a>"},"day":"01","page":"45 - 57","publisher":"Elsevier","status":"public","year":"2017","oa":1,"date_published":"2017-01-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}