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

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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

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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.
License of this version: CC BY 4.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2019
Appears in Collections:Fakultät für Mathematik und Physik

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pos. country downloads
total perc.
1 image of flag of Germany Germany 16 76.19%
2 image of flag of United States United States 2 9.52%
3 image of flag of Sweden Sweden 1 4.76%
4 image of flag of Russian Federation Russian Federation 1 4.76%
5 image of flag of France France 1 4.76%

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