Web spaces and worldwide web spaces: Topological aspects of domain theory

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dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/10440
dc.identifier.uri https://doi.org/10.15488/10366
dc.contributor.author Erné, Marcel
dc.date.accessioned 2021-02-04T08:11:52Z
dc.date.available 2021-02-04T08:11:52Z
dc.date.issued 2019
dc.identifier.citation Erné, M.: Web spaces and worldwide web spaces: Topological aspects of domain theory. In: Logical Methods in Computer Science 15 (2019), Nr. 1, S. 23:1-23:38. DOI: https://doi.org/10.23638/LMCS-15(1:23)2019
dc.description.abstract 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, where a fan is 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 T0 web spaces are exactly the generalized Scott spaces associated with locally approximating ideal extensions, and the T0 C-spaces are exactly the generalized Scott spaces associated with globally approximating and interpolating ideal extensions. The characterization of continuous lattices as meet-continuous lattices with T2 Lawson topology and the Fundamental Theorem of Compact Semilattices are extended to non-complete posets. Finally, cardinal invariants like density and weight of the involved objects are investigated. © 2019 Marcel Erné. All rights reserved. eng
dc.language.iso eng
dc.publisher Braunschweig : Department of Theoretical Computer Science, Technical University of Braunschweig
dc.relation.ispartofseries Logical Methods in Computer Science 15 (2019), Nr. 1
dc.rights CC BY 4.0 Unported
dc.rights.uri https://creativecommons.org/licenses/by/4.0/
dc.subject web spaces eng
dc.subject worldwide web eng
dc.subject domain eng
dc.subject.ddc 004 | Informatik ger
dc.title Web spaces and worldwide web spaces: Topological aspects of domain theory
dc.type article
dc.type Text
dc.relation.issn 1860-5974
dc.relation.doi https://doi.org/10.23638/LMCS-15(1:23)2019
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 15
dc.bibliographicCitation.firstPage 23:1
dc.bibliographicCitation.lastPage 23:38
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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