Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Effective Domains and Admissible Domain Representations
Department of Mathematics, Uppsala university. (Mathematical logic)ORCID iD: 0000-0003-4256-2960
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

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
Supervisors
Note

QC 20180109

Available from: 2018-01-09 Created: 2018-01-09 Last updated: 2018-01-10Bibliographically approved
List of papers
1. Cartesian closed categories of effective domains
Open this publication in new window or tab >>Cartesian closed categories of effective domains
2002 (English)In: Proof and System-Reliability, 2002, p. 1-20Chapter in book (Refereed)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-220934 (URN)1-4020-0607-1 (ISBN)
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10Bibliographically approved
2. Two categories of effective continuous cpos
Open this publication in new window or tab >>Two categories of effective continuous cpos
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-220935 (URN)
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10Bibliographically approved
3. Admissible domain representations of topological spaces
Open this publication in new window or tab >>Admissible domain representations of topological spaces
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-220936 (URN)
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10Bibliographically approved
4. Admissible domain representations of convergence spaces
Open this publication in new window or tab >>Admissible domain representations of convergence spaces
(English)Manuscript (preprint) (Other academic)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-220937 (URN)
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10Bibliographically approved

Open Access in DiVA

fulltext(214 kB)19 downloads
File information
File name FULLTEXT01.pdfFile size 214 kBChecksum SHA-512
3f36bd04b0d4d865097d599d3bc04a8d117cd4f7254f49b246f9d6096b505fe545c33f2bf7e9d1a5f10266a4cf77a6d193a6fdfbd341ab89ba1bf410c6f0fd71
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Hamrin, Göran
MathematicsAlgebra and Logic

Search outside of DiVA

GoogleGoogle Scholar
Total: 19 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 103 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf