---
_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).
corr_author: '1'
date_created: 2023-09-24T22:01:11Z
date_published: 2023-10-25T00:00:00Z
date_updated: 2024-10-09T21:07:00Z
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'
...