--- _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' ...