Equilogical Spaces and Convergence Spaces (Reinhold Heckmann)

Equilogical spaces and convergence spaces form two categories EQU and CONV, respectively, that contain the category TOP of topological spaces as a full subcategory. In contrast to TOP, they are cartesian closed, i.e. admit the construction of function spaces in a way suitable for the interpretation of lambda-calculus. Note that some people, including myself in earlier papers, say filter spaces (FIL) instead of convergence spaces (CONV).

• Separation Classes of Equilogical Spaces,
  Proceedings of the Workshop on Domains IV (Rolandseck, Oct. 1998),
  Technical report Nr. 99-01 of the Fachgruppe Informatik of Universität-Gesamthochschule Siegen, 115-128 (1999)
  [Abstract] [Paper.ps.gz (13p, 52k)]
  

• Ordered Equilogical Spaces and Equilogical D-Spaces,
  This was the original submission to MFPS '99. It was later modified and extended (see below).
  [Abstract] [Paper.ps.gz (11p, 52k)]

• Completeness Classes of Equilogical Spaces,
  MFPS '99, New Orleans, April 1999.
  Electronic Notes in Theoretical Computer Science, Vol. 20 (1999)
  URL: http://www.elsevier.nl/locate/entcs/volume20.html
  [Abstract] [Paper.ps.gz (16p, 65k)]

• On the Relationship between Filter Spaces and Equilogical Spaces,
  Draft report,
  [Abstract] [Paper.ps.gz (10p, 48k)]

• A Non-Topological View of Dcpo's as Convergence Spaces,
  presented at Dagstuhl Seminar Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitalization (June 2000) and First Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2000) (July 2000).
  
  • Slides of the talk:    1 per page: [Slides.ps.gz (16p, 52k)]    4 per page: [Slides4.ps.gz (4p, 54k)]
    
  • Extended abstract: Electronic Notes in Theoretical Computer Science, Vol. 40 (2002)
    URL: http://www.elsevier.nl/locate/entcs/volume40.html
    [Abstract] [Paper.ps.gz (22p, 128k)]
    
  • Full paper: Theoretical Computer Science, Vol. 305, 159 - 186 (2003)
    [Abstract] [Paper.ps.gz (27p, 136k, reformatted)] [Paper.pdf (27p, 268k, reformatted)]
    

• Domain Representations of Convergence Spaces,
  presented at Dagstuhl Seminar Mathematical Structures for Computable Topology and Geometry (May 2002).
  Slides of the talk:    1 per page: [Slides.ps.gz (16p, 90k)]    4 per page: [Slides4.ps.gz (4p, 91k)]
  

• A Cartesian Closed Extension of the Category of Locales,
  to be presented at Dagstuhl Seminar Spatial Representation: Discrete vs.Continuous Computational Models (August 2004)
  and at DOMAINS VII, Darmstadt, August 29 - September 1, 2004.
  [Abstract]
  Extended Abstract (1 page): [ExtAbs.ps] [ExtAbs.pdf]
  Full paper (20 pages): [Paper.ps.gz] [Paper.pdf]
  

• Injective Convergence and Equilogical Spaces via Pretopological Spaces,
  Presented at MFPS XXI
  Proceedings of the 21st Annual Conference on Mathematical Foundations of Programming Semantics (MFPS XXI)
  Birmingham, UK, 18-21 May 2005. Edited by M. Escardó, A. Jung and M. Mislove
  Electronic Notes in Theoretical Computer Science, Vol. 155 (2006)
  (Paper updated at 30 Aug 2006 to version from 25 Oct 2005)
  [Abstract] [Paper.ps.gz (19p, 140k)] [Paper.pdf (19p, 312k)]