---
_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
arxiv: 1
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. <i>Theoretical Computer Science</i>. 2023;977. doi:<a
    href="https://doi.org/10.1016/j.tcs.2023.114129">10.1016/j.tcs.2023.114129</a>
  apa: Castellano, I., Giordano Bruno, A., &#38; Zava, N. (2023). Weakly weighted
    generalised quasi-metric spaces and semilattices. <i>Theoretical Computer Science</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.tcs.2023.114129">https://doi.org/10.1016/j.tcs.2023.114129</a>
  chicago: Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted
    Generalised Quasi-Metric Spaces and Semilattices.” <i>Theoretical Computer Science</i>.
    Elsevier, 2023. <a href="https://doi.org/10.1016/j.tcs.2023.114129">https://doi.org/10.1016/j.tcs.2023.114129</a>.
  ieee: I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised
    quasi-metric spaces and semilattices,” <i>Theoretical Computer Science</i>, 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.” <i>Theoretical Computer Science</i>, vol. 977, 114129, Elsevier,
    2023, doi:<a href="https://doi.org/10.1016/j.tcs.2023.114129">10.1016/j.tcs.2023.114129</a>.
  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: '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. <i>Quaestiones Mathematicae</i>. 2023;46(S1):191-221.
    doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a>
  apa: Dikranjan, D., Giordano Bruno, A., &#38; Zava, N. (2023). Epimorphisms and
    closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>.
    Taylor &#38; Francis. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a>
  chicago: Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure
    Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>. Taylor
    &#38; Francis, 2023. <a href="https://doi.org/10.2989/16073606.2023.2247731">https://doi.org/10.2989/16073606.2023.2247731</a>.
  ieee: D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators
    of categories of semilattices,” <i>Quaestiones Mathematicae</i>, vol. 46, no.
    S1. Taylor &#38; 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.” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1, Taylor &#38;
    Francis, 2023, pp. 191–221, doi:<a href="https://doi.org/10.2989/16073606.2023.2247731">10.2989/16073606.2023.2247731</a>.
  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: '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. <i>Topology and its Applications</i>. 2022;309. doi:<a href="https://doi.org/10.1016/j.topol.2021.107916">10.1016/j.topol.2021.107916</a>
  apa: Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., &#38; Toller, D.
    (2022). Generalized quasi-metric semilattices. <i>Topology and Its Applications</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.topol.2021.107916">https://doi.org/10.1016/j.topol.2021.107916</a>
  chicago: Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava,
    and Daniele Toller. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its
    Applications</i>. Elsevier, 2022. <a href="https://doi.org/10.1016/j.topol.2021.107916">https://doi.org/10.1016/j.topol.2021.107916</a>.
  ieee: D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized
    quasi-metric semilattices,” <i>Topology and its Applications</i>, 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.” <i>Topology
    and Its Applications</i>, vol. 309, 107916, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.topol.2021.107916">10.1016/j.topol.2021.107916</a>.
  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. <i>European Journal of Mathematics</i>. 2021. doi:<a href="https://doi.org/10.1007/s40879-021-00515-3">10.1007/s40879-021-00515-3</a>
  apa: Weighill, T., Yamauchi, T., &#38; Zava, N. (2021). Coarse infinite-dimensionality
    of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s40879-021-00515-3">https://doi.org/10.1007/s40879-021-00515-3</a>
  chicago: Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality
    of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s40879-021-00515-3">https://doi.org/10.1007/s40879-021-00515-3</a>.
  ieee: T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of
    hyperspaces of finite subsets,” <i>European Journal of Mathematics</i>. 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.” <i>European Journal of Mathematics</i>, Springer Nature, 2021,
    doi:<a href="https://doi.org/10.1007/s40879-021-00515-3">10.1007/s40879-021-00515-3</a>.
  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
license: https://creativecommons.org/licenses/by/4.0/
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'
...