---
_id: '521'
abstract:
- lang: eng
  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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Kyle
  full_name: Austin, Kyle
  last_name: Austin
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
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>
  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>
  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>.
  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.
  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.
corr_author: '1'
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2025-09-18T09:47:04Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
external_id:
  arxiv:
  - '1608.03954'
  isi:
  - '000390501400005'
intvolume: '       215'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.03954
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 215
year: '2017'
...