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Contributions to Pointfree Topology and Apartness SpacesPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2011 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala: Department of Mathematics , 2011. , 40 p.
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 71
##### Keyword [en]

Constructive mathematics, General topology, Pointfree topology, Domain theory, Interval analysis, Apartness spaces
##### National Category

Algebra and Logic
##### Research subject

Mathematical Logic
##### Identifiers

URN: urn:nbn:se:uu:diva-152068ISBN: 978-91-506-2219-5 (print)OAI: oai:DiVA.org:uu-152068DiVA: diva2:412415
##### Public defence

2011-06-08, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt542",{id:"formSmash:j_idt542",widgetVar:"widget_formSmash_j_idt542",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt548",{id:"formSmash:j_idt548",widgetVar:"widget_formSmash_j_idt548",multiple:true});
Available from: 2011-05-17 Created: 2011-04-23 Last updated: 2011-06-14Bibliographically approved
##### List of papers

The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion of a domain representation of a formal space as a way to introduce generalized points of the represented space, whereas we in Paper II give a constructive and point-free treatment of the domain theoretic approach to differential calculus. The last two papers are of a slightly different nature but still concern constructive topology. In paper III we consider a measure theoretic covering theorem from various constructive angles in both point-set and point-free topology. We prove a point-free version of the theorem. In Paper IV we deal with issues of impredicativity in the theory of apartness spaces. We introduce a notion of set-presented apartness relation which enables a predicative treatment of basic constructions of point-set apartness spaces.

1. Local Scott compactification$(function(){PrimeFaces.cw("OverlayPanel","overlay412411",{id:"formSmash:j_idt584:0:j_idt589",widgetVar:"overlay412411",target:"formSmash:j_idt584:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. The domain theoretic derivative in formal topology$(function(){PrimeFaces.cw("OverlayPanel","overlay412412",{id:"formSmash:j_idt584:1:j_idt589",widgetVar:"overlay412412",target:"formSmash:j_idt584:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. The Vitali covering theorem in constructive mathematics$(function(){PrimeFaces.cw("OverlayPanel","overlay412413",{id:"formSmash:j_idt584:2:j_idt589",widgetVar:"overlay412413",target:"formSmash:j_idt584:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Towards set-presentable apartness spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay412414",{id:"formSmash:j_idt584:3:j_idt589",widgetVar:"overlay412414",target:"formSmash:j_idt584:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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