---
_id: '737'
abstract:
- lang: eng
  text: We generalize Brazas’ topology on the fundamental group to the whole universal
    path space X˜ i.e., to the set of homotopy classes of all based paths. We develop
    basic properties of the new notion and provide a complete comparison of the obtained
    topology with the established topologies, in particular with the Lasso topology
    and the CO topology, i.e., the topology that is induced by the compact-open topology.
    It turns out that the new topology is the finest topology contained in the CO
    topology, for which the action of the fundamental group on the universal path
    space is a continuous group action.
article_processing_charge: No
author:
- first_name: Ziga
  full_name: Virk, Ziga
  id: 2E36B656-F248-11E8-B48F-1D18A9856A87
  last_name: Virk
- first_name: Andreas
  full_name: Zastrow, Andreas
  last_name: Zastrow
citation:
  ama: Virk Z, Zastrow A. A new topology on the universal path space. <i>Topology
    and its Applications</i>. 2017;231:186-196. doi:<a href="https://doi.org/10.1016/j.topol.2017.09.015">10.1016/j.topol.2017.09.015</a>
  apa: Virk, Z., &#38; Zastrow, A. (2017). A new topology on the universal path space.
    <i>Topology and Its Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.topol.2017.09.015">https://doi.org/10.1016/j.topol.2017.09.015</a>
  chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
    Space.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href="https://doi.org/10.1016/j.topol.2017.09.015">https://doi.org/10.1016/j.topol.2017.09.015</a>.
  ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” <i>Topology
    and its Applications</i>, vol. 231. Elsevier, pp. 186–196, 2017.
  ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology
    and its Applications. 231, 186–196.
  mla: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.”
    <i>Topology and Its Applications</i>, vol. 231, Elsevier, 2017, pp. 186–96, doi:<a
    href="https://doi.org/10.1016/j.topol.2017.09.015">10.1016/j.topol.2017.09.015</a>.
  short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:53:01Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2017.09.015
external_id:
  isi:
  - '000413889100012'
intvolume: '       231'
isi: 1
language:
- iso: eng
month: '11'
oa_version: None
page: 186 - 196
publication: Topology and its Applications
publication_identifier:
  issn:
  - '01668641'
publication_status: published
publisher: Elsevier
publist_id: '6930'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new topology on the universal path space
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 231
year: '2017'
...
---
_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.
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.
date_created: 2018-12-11T11:46:56Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2021-01-12T08:01:21Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.topol.2016.10.005
intvolume: '       215'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1608.03954v1
month: '01'
oa: 1
oa_version: Submitted Version
page: 45 - 57
publication: Topology and its Applications
publication_identifier:
  issn:
  - '01668641'
publication_status: published
publisher: Elsevier
publist_id: '7299'
quality_controlled: '1'
status: public
title: Higson compactification and dimension raising
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 215
year: '2017'
...