Higson compactification and dimension raising

K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.


Journal Article | Published | English
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;
Department
Abstract
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.
Publishing Year
Date Published
2017-01-01
Journal Title
Topology and its Applications
Volume
215
Page
45 - 57
ISSN
IST-REx-ID

Cite this

Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications, 215, 45–57. https://doi.org/10.1016/j.topol.2016.10.005
Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications 215 (2017): 45–57. https://doi.org/10.1016/j.topol.2016.10.005.
K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215, pp. 45–57, 2017.
Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.
Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.

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