---
_id: '14557'
abstract:
- lang: eng
text: Motivated by a problem posed in [10], we investigate the closure operators
of the category SLatt of join semilattices and its subcategory SLattO of join
semilattices with bottom element. In particular, we show that there are only finitely
many closure operators of both categories, and provide a complete classification.
We use this result to deduce the known fact that epimorphisms of SLatt and SLattO
are surjective. We complement the paper with two different proofs of this result
using either generators or Isbell’s zigzag theorem.
acknowledgement: "The first and second named authors are members of GNSAGA – INdAM.\r\nThe
third named author was supported by the FWF Grant, Project number I4245–N35"
article_processing_charge: No
article_type: original
author:
- first_name: D.
full_name: Dikranjan, D.
last_name: Dikranjan
- first_name: A.
full_name: Giordano Bruno, A.
last_name: Giordano Bruno
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of
categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221.
doi:10.2989/16073606.2023.2247731
apa: Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and
closure operators of categories of semilattices. Quaestiones Mathematicae.
Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731
chicago: Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure
Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor
& Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731.
ieee: D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators
of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no.
S1. Taylor & Francis, pp. 191–221, 2023.
ista: Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators
of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.
mla: Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of
Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor &
Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731.
short: D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023)
191–221.
date_created: 2023-11-19T23:00:55Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-11-20T09:24:48Z
day: '01'
department:
- _id: HeEd
doi: 10.2989/16073606.2023.2247731
intvolume: ' 46'
issue: S1
language:
- iso: eng
month: '11'
oa_version: None
page: 191-221
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I04245
name: Algebraic Footprints of Geometric Features in Homology
publication: Quaestiones Mathematicae
publication_identifier:
eissn:
- 1727-933X
issn:
- 1607-3606
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Epimorphisms and closure operators of categories of semilattices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2023'
...
---
_id: '14362'
abstract:
- lang: eng
text: "Motivated by recent applications to entropy theory in dynamical systems,
we generalise notions introduced by Matthews and define weakly weighted and componentwise
weakly weighted (generalised) quasi-metrics. We then systematise and extend to
full generality the correspondences between these objects and other structures
arising in theoretical computer science and dynamics. In particular, we study
the correspondences with weak partial metrics and, if the underlying space is
a semilattice, with invariant (generalised) quasi-metrics satisfying the descending
path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude
discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation
of both the known intrinsic semilattice entropy and the semigroup entropy."
article_number: '114129'
article_processing_charge: No
article_type: original
author:
- first_name: Ilaria
full_name: Castellano, Ilaria
last_name: Castellano
- first_name: Anna
full_name: Giordano Bruno, Anna
last_name: Giordano Bruno
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
orcid: 0000-0001-8686-1888
citation:
ama: Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric
spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129
apa: Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted
generalised quasi-metric spaces and semilattices. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/j.tcs.2023.114129
chicago: Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted
Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science.
Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.
ieee: I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised
quasi-metric spaces and semilattices,” Theoretical Computer Science, vol.
977. Elsevier, 2023.
ista: Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised
quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.
mla: Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces
and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier,
2023, doi:10.1016/j.tcs.2023.114129.
short: I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977
(2023).
date_created: 2023-09-24T22:01:11Z
date_published: 2023-10-25T00:00:00Z
date_updated: 2024-01-30T13:22:04Z
day: '25'
department:
- _id: HeEd
doi: 10.1016/j.tcs.2023.114129
external_id:
arxiv:
- '2212.08424'
isi:
- '001076934000001'
intvolume: ' 977'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2212.08424 '
month: '10'
oa: 1
oa_version: Preprint
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weakly weighted generalised quasi-metric spaces and semilattices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 977
year: '2023'
...
---
_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).
date_created: 2021-12-05T23:01:44Z
date_published: 2022-03-15T00:00:00Z
date_updated: 2023-08-02T13:33:24Z
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: '10608'
abstract:
- lang: eng
text: We consider infinite-dimensional properties in coarse geometry for hyperspaces
consisting of finite subsets of metric spaces with the Hausdorff metric. We see
that several infinite-dimensional properties are preserved by taking the hyperspace
of subsets with at most n points. On the other hand, we prove that, if a metric
space contains a sequence of long intervals coarsely, then its hyperspace of finite
subsets is not coarsely embeddable into any uniformly convex Banach space. As
a corollary, the hyperspace of finite subsets of the real line is not coarsely
embeddable into any uniformly convex Banach space. It is also shown that every
(not necessarily bounded geometry) metric space with straight finite decomposition
complexity has metric sparsification property.
acknowledgement: We would like to thank the referees for their careful reading and
the comments that improved our work. The third named author would like to thank
the Division of Mathematics, Physics and Earth Sciences of the Graduate School of
Science and Engineering of Ehime University and the second named author for hosting
his visit in June 2018. Open access funding provided by Institute of Science and
Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Thomas
full_name: Weighill, Thomas
last_name: Weighill
- first_name: Takamitsu
full_name: Yamauchi, Takamitsu
last_name: Yamauchi
- first_name: Nicolò
full_name: Zava, Nicolò
id: c8b3499c-7a77-11eb-b046-aa368cbbf2ad
last_name: Zava
citation:
ama: Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3
apa: Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality
of hyperspaces of finite subsets. European Journal of Mathematics. Springer
Nature. https://doi.org/10.1007/s40879-021-00515-3
chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality
of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer
Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.
ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of
hyperspaces of finite subsets,” European Journal of Mathematics. Springer
Nature, 2021.
ista: Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces
of finite subsets. European Journal of Mathematics.
mla: Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of
Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021,
doi:10.1007/s40879-021-00515-3.
short: T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).
date_created: 2022-01-09T23:01:27Z
date_published: 2021-12-30T00:00:00Z
date_updated: 2022-01-10T08:36:55Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1007/s40879-021-00515-3
file:
- access_level: open_access
checksum: c435dcfa1ad3aadc5cdd7366bc7f4e98
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-10T08:33:22Z
date_updated: 2022-01-10T08:33:22Z
file_id: '10610'
file_name: 2021_EuJournalMath_Weighill.pdf
file_size: 384908
relation: main_file
success: 1
file_date_updated: 2022-01-10T08:33:22Z
has_accepted_license: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coarse infinite-dimensionality of hyperspaces of finite subsets
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2021'
...