{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:59Z","timestamp":1753889939129,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T00:00:00Z","timestamp":1565222400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T00:00:00Z","timestamp":1565222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,8,8]],"date-time":"2019-08-08T00:00:00Z","timestamp":1565222400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We investigate powerspace constructions on topological spaces, with a particular focus on the category of quasi-Polish spaces. We show that the upper and lower powerspaces commute on all quasi-Polish spaces, and show more generally that this commutativity is equivalent to the topological property of consonance. We then investigate powerspace constructions on the open set lattices of quasi-Polish spaces, and provide a complete characterization of how the upper and lower powerspaces distribute over the open set lattice construction.<\/jats:p>","DOI":"10.23638\/lmcs-15(3:13)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:02Z","timestamp":1743701642000},"source":"Crossref","is-referenced-by-count":0,"title":["On the commutativity of the powerspace constructions"],"prefix":"10.23638","volume":"Volume 15, Issue 3","author":[{"given":"Matthew","family":"de Brecht","sequence":"first","affiliation":[]},{"given":"Tatsuji","family":"Kawai","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,8,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1709.06226v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1709.06226v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:02Z","timestamp":1743701642000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3945"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(3:13)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1709.06226v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1709.06226v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1709.06226","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1709.06226","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,8,8]]},"article-number":"3945"}}