---
_id: '10413'
abstract:
- lang: eng
text: Motivated by the recent introduction of the intrinsic semilattice entropy,
we study generalized quasi-metric semilattices and their categories. We investigate
the relationship between these objects and generalized semivaluations, extending
Nakamura and Schellekens' approach. Finally, we use this correspondence to compare
the intrinsic semilattice entropy and the semigroup entropy induced in particular
situations, like sets, torsion abelian groups and vector spaces.
acknowledgement: Dedicated to the memory of Hans-Peter Künzi.
article_number: '107916'
article_processing_charge: No
article_type: original
author:
- first_name: Dikran
full_name: Dikranjan, Dikran
last_name: Dikranjan
- first_name: Anna
full_name: Giordano Bruno, Anna
last_name: Giordano Bruno
- first_name: Hans Peter
full_name: Künzi, Hans Peter
last_name: Künzi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
- first_name: Daniele
full_name: Toller, Daniele
last_name: Toller
citation:
ama: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric
semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916
apa: Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D.
(2022). Generalized quasi-metric semilattices. Topology and Its Applications.
Elsevier. https://doi.org/10.1016/j.topol.2021.107916
chicago: Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava,
and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its
Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916.
ieee: D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized
quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier,
2022.
ista: Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized
quasi-metric semilattices. Topology and its Applications. 309, 107916.
mla: Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology
and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916.
short: D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology
and Its Applications 309 (2022).
corr_author: '1'
date_created: 2021-12-05T23:01:44Z
date_published: 2022-03-15T00:00:00Z
date_updated: 2024-10-09T21:01:16Z
day: '15'
department:
- _id: HeEd
doi: 10.1016/j.topol.2021.107916
external_id:
isi:
- '000791838800012'
intvolume: ' 309'
isi: 1
language:
- iso: eng
month: '03'
oa_version: None
publication: Topology and its Applications
publication_identifier:
issn:
- 0166-8641
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalized quasi-metric semilattices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 309
year: '2022'
...
---
_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. Topology
and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005
apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005
chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.”
Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.
ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology
and its Applications, 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.”
Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.
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'
...
---
_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. Topology
and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
apa: Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space.
Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015
chicago: Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path
Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.
ieee: Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology
and its Applications, 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.”
Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.
short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.
corr_author: '1'
date_created: 2018-12-11T11:48:14Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2026-04-16T10:04:39Z
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:
- 0166-8641
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 231
year: '2017'
...