{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:44Z","timestamp":1753889924897,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"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>Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology with a second topology having the dual specialization order; these patch spaces possess good convexity and separation properties and determine the original web spaces. The category of C-spaces is concretely isomorphic to the category of fan spaces; these are certain quasi-ordered spaces having neighborhood bases of fans, obtained by deleting a finite number of principal dual ideals from a principal dual ideal. Our approach has useful consequences for domain theory, because the T$_0$ web spaces are exactly the generalized Scott spaces of locally approximating ideal extensions, and the T$_0$ C-spaces are exactly the generalized Scott spaces of globally approximating and interpolating ideal extensions. We extend the characterization of continuous lattices as meet-continuous lattices with T$_2$ Lawson topology and the Fundamental Theorem of Compact Semilattices to non-complete posets. Finally, cardinal invariants like density and weight of the involved objects are investigated.<\/jats:p><jats:p>Comment: 36 pages, 1 figure, 8 diagrams. arXiv admin note: text overlap with   arXiv:1607.04721<\/jats:p>","DOI":"10.23638\/lmcs-15(1:23)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:31Z","timestamp":1743701311000},"source":"Crossref","is-referenced-by-count":0,"title":["Web spaces and worldwide web spaces: topological aspects of domain theory"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"given":"Marcel","family":"Ern\u00e9","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,3,5]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1802.08170v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1802.08170v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:31Z","timestamp":1743701311000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/1539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,5]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:23)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1802.08170v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.04721v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1802.08170","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1802.08170","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,3,5]]},"article-number":"1539"}}