A non-topological view of dcpos as convergence spaces

Theoretical Computer Science

Volumn 305, Issue 1-3, 2003, Pages 159-186

  Heckmann, Reinhold ^a  

^a AbsInt Angewandte Informatik GmbH   (Germany)

Author keywords

Convergence spaces; Domains; Function spaces; Topology

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EMBEDDED SYSTEMS; FUNCTIONS; TOPOLOGY;

COTOPOLOGICAL CONVERGENCE STRUCTURES;

COMPUTER SCIENCE;

EID: 0041528439     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00706-5     Document Type: Conference Paper

References (19)

1. A. Bauer, L. Birkedal, D.S. Scott, Equilogical spaces, Theoret. Comput. Sci. 1998 (revised 2001), URL: http://www.cs.cmu.edu/Groups/LTC/, to appear.
2. G. Bourdaud, Some cartesian closed categories of convergence spaces, in: Categorical Topology, Proc. Conf. Mannheim, 1975, Lecture Notes in Mathematics, Vol. 540, Springer, Berlin, 1976, pp. 93-108.
3. Erné Marcel Scott convergence and Scott topology in partially ordered sets II. Banaschewski B., Hoffmann R.-E. Continuous Lattices, Proc. Conf. Bremen, 1979. Lecture Notes in Mathematics. Vol. 871:1981;61-96 Springer, Berlin.
4. Ershov Yu.L. On. d-spaces Theoret. Comput. Sci. 224:1999;59-72.
5. Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M., Scott D.S. A Compendium of Continuous Lattices. 1980;Springer, Berlin.
6. R. Heckmann, Spaces of valuations, in: S. Andima, R.C. Flagg, G. Itzkowitz, Y. Kong, R. Kopperman, P. Misra (Eds.), Papers on General Topology and its Applications, Annals of the New York Academy of Sciences, New York, Vol. 806, December 1996, pp. 174-200.
7. R. Heckmann, On the relationship between filter spaces and equilogical spaces, URL: http://www.cs.uni-sb.de/̃heckmann/papers/fil.ps.gz, December 1998.
8. R. Heckmann, M. Huth, A duality theory for quantitative semantics, in: Computer Science Logic CSL'97 (Selected Papers), Lecture Notes in Computer Science, Vol. 1414, Springer, Berlin, 1998, pp. 255-274.
9. Heckmann R., Huth M. Quantitative semantics, topology, and possibility measures. Topology Appl. 89(1-2):1998;151-178.
10. Herrlich H., Nel L.D. Cartesian closed topological hulls. Proc. AMS. 62:1977;215-222.
11. Hyland J.M.E. Continuity in spatial toposes. Dold A., Eckmann B. Applications of Sheaves. Lecture Notes in Mathematics. Vol. 753:1977;442-465 Springer, Berlin.
12. Hyland J.M.E. Filter spaces and continuous functionals. Ann. Math. Logic. 16:1979;101-143.
13. Isbell J.R. Completion of a construction of Johnstone. Proc. AMS. 85:1982;333-334.
14. L.D. Nel, Cartesian closed topological categories, in: Categorical Topology, Proc. Conf. Mannheim 1975, Lecture Notes in Mathematics, Vol. 540, Springer, Berlin, 1976, pp. 439-451.
15. Schwarz F., Weck S. Scott topology, Isbell topology, and continuous convergence. Hoffmann R.-E., Hofmann K.H. Continuous Lattices and their Applications. 1985;251-271 Marcel Dekker, New York.
16. D.S. Scott, A new category? Domains, spaces, and equivalence relations, URL: http://www.cs.cmu.edu/Groups/LTC/, 1996.
17. Weck S. Scott convergence and Scott topology in partially ordered sets I. Banaschewski B., Hoffmann R.-E. Continuous Lattices, Proc. Conf. Bremen, 1979. Lecture Notes in Mathematics. Vol. 871:1981;372-383 Springer, Berlin.
18. O. Wyler, Filter space monads, regularity, completions, in: R. Alo, R.W. Heath, J. Nagata (Eds.), TOPO 72 - General Topology and its Applications, Lecture Notes in Mathematics, Vol. 378, Springer, Berlin, 1974, pp. 591-637.
19. Wyler O. Dedekind complete posets and Scott topologies. Banaschewski B., Hoffmann R.-E. Continuous Lattices, Proc. Conf. Bremen 1979. Lecture Notes in Mathematics. Vol. 871:1981;384-389 Springer, Berlin.