Contributions to Pointfree Topology and Apartness Spaces
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
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.
Place, publisher, year, edition, pages
Uppsala: Department of Mathematics , 2011. , 40 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 71
Constructive mathematics, General topology, Pointfree topology, Domain theory, Interval analysis, Apartness spaces
Algebra and Logic
Research subject Mathematical Logic
IdentifiersURN: urn:nbn:se:uu:diva-152068ISBN: 978-91-506-2219-5OAI: oai:DiVA.org:uu-152068DiVA: diva2:412415
2011-06-08, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
Schuster, Peter, Privatdozent Dr
Palmgren, Erik, ProfessorStoltenberg-Hansen, Viggo, Professor em
List of papers