{"date_updated":"2024-01-30T13:22:04Z","article_processing_charge":"No","month":"10","day":"25","type":"journal_article","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."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.08424 "}],"department":[{"_id":"HeEd"}],"publication_status":"published","date_published":"2023-10-25T00:00:00Z","scopus_import":"1","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-09-24T22:01:11Z","oa":1,"oa_version":"Preprint","status":"public","title":"Weakly weighted generalised quasi-metric spaces and semilattices","quality_controlled":"1","publication_identifier":{"issn":["0304-3975"]},"external_id":{"arxiv":["2212.08424"],"isi":["001076934000001"]},"doi":"10.1016/j.tcs.2023.114129","author":[{"last_name":"Castellano","first_name":"Ilaria","full_name":"Castellano, Ilaria"},{"full_name":"Giordano Bruno, Anna","first_name":"Anna","last_name":"Giordano Bruno"},{"orcid":"0000-0001-8686-1888","last_name":"Zava","first_name":"Nicolò","full_name":"Zava, Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"publication":"Theoretical Computer Science","language":[{"iso":"eng"}],"article_number":"114129","_id":"14362","citation":{"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.","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).","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>","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.","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>."},"article_type":"original","year":"2023","volume":977,"intvolume":"       977","isi":1}