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Effective Domains and Admissible Domain RepresentationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2005 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Uppsala universitet, 2005. , p. vii + 33 p.
##### Series

Uppsala dissertations in Mathematics, ISSN 1401-2049 ; 42
##### Keywords [en]

Logic, symbolic and mathematical, domain theory, admissible domain representation, cartesian closure, effective domains, κ-sequential space, limit space, Matematisk logik
##### National Category

Mathematics Algebra and Logic
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-220918ISBN: 91-506-1817-2 (print)OAI: oai:DiVA.org:kth-220918DiVA, id: diva2:1172235
##### Public defence

2005-09-07, 00:00
##### Opponent

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#####

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##### Note

##### List of papers

This thesis consists of four papers in domain theory and a summary. The first two papers deal with the problem of defining effectivity for continuous cpos. The third and fourth paper present the new notion of an admissible domain representation, where a domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to X via a continuous function from E to D. In Paper I we define a cartesian closed category of effective bifinite domains. We also investigate the method of inducing effectivity onto continuous cpos via projection pairs, resulting in a cartesian closed category of projections of effective bifinite domains. In Paper II we introduce the notion of an almost algebraic basis for a continuous cpo, showing that there is a natural cartesian closed category of effective consistently complete continuous cpos with almost algebraic bases. We also generalise the notion of a complete set, used in Paper I to define the bifinite domains, and investigate what closure results that can be obtained. In Paper III we consider admissible domain representations of topological spaces. We present a characterisation theorem of exactly when a topological space has a λ-admissible and κ-based domain representation. We also show that there is a natural cartesian closed category of countably based and countably admissible domain representations. In Paper IV we consider admissible domain representations of convergence spaces, where a convergence space is a set X together with a convergence relation between nets on X and elements of X. We study in particular the new notion of weak κ-convergence spaces, which roughly means that the convergence relation satisfies a generalisation of the Kuratowski limit space axioms to cardinality κ. We show that the category of weak κ-convergence spaces is cartesian closed. We also show that the category of weak κ-convergence spaces that have a dense, λ-admissible, κ-continuous and α-based consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ. As natural corollaries we obtain corresponding results for the associated category of weak convergence spaces.

QC 20180109

Available from: 2018-01-09 Created: 2018-01-09 Last updated: 2018-01-10Bibliographically approved1. Cartesian closed categories of effective domains$(function(){PrimeFaces.cw("OverlayPanel","overlay1172421",{id:"formSmash:j_idt538:0:j_idt542",widgetVar:"overlay1172421",target:"formSmash:j_idt538:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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