Stably compact spaces and the probabilistic powerspace construction

Electronic Notes in Theoretical Computer Science

Volumn 87, Issue , 2004, Pages 5-20

  Jung, Achim ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Compact ordered space; Domain theory; Probabilistic power domain; Stably compact domain

Indexed keywords

COMPUTATIONAL COMPLEXITY; PROBABILITY; SET THEORY; TOPOLOGY;

COMPACT ORDERED SPACE; DOMAIN THEORY; PROBABILISTIC POWER DOMAIN; STABLY COMPACT DOMAIN;

COMPUTER SCIENCE;

EID: 9544225976     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2004.10.001     Document Type: Conference Paper

References (28)

1. S. Abramsky. Domain theory in logical form. In Symposium on Logic In Computer Science, pages 47-53. IEEE Computer Society Press, 1987.
2. S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic, in Computer Science, volume 3, pages 1-168. Clarendon Press, 1994.
3. M. Alvarez-Manilla. Measure theoretic results for continuous valuations on partially ordered spaces. PhD thesis, Imperial College, University of London, 2001.
4. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. A Compendium of Continuous Lattices. Springer Verlag, 1980.
5. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott. Continuous Lattices and Domains, volume 93 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2003. Revised and expanded edition of [4].
6. R. Heckmann. Spaces of valuations. In S. Andima, R. C. Flagg, G. Itzkowitz, P. Misra, Y. Kong, and R. Kopperman, editors, Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine, volume 806 of Annals of the New York Academy of Sciences, pages 174-200, 1996.
7. A. Jung, M. Kegelmann, and M. A. Moshier. Multi lingual sequent calculus and coherent spaces. In S. Brookes and M. Mislove, editors, 13th Conference on Mathematical Foundations of Programming Semantics, volume 6 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 1997. 18 pages.
8. A. Jung, M. Kegelmann, and M. A. Moshier. Multi lingual sequent calculus and coherent spaces. Fundamenta Informaticae, 37:369-412, 1999.
9. A. Jung, M. Kegelmann, and M. A. Moshier. Stably compact spaces and closed relations. In S. Brookes and M. Mislove, editors, 17th Conference on Mathematical Foundations of Programming Semantics, volume 45 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 2001. 24 pages.
10. C. Jones. Probabilistic Non-Determinism. PhD thesis. University of Edinburgh, Edinburgh, 1990.
11. Also published as Technical Report No. CST-63-90.
12. C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the 4th Annual Symposium on Logic in Computer Science, pages 186-195. IEEE Computer Society Press, 1989.
13. A. Jung and Ph. Sünderhauf. On the duality of compact vs. open. In S. Andima, R. C. Flagg, G. Itzkowitz, P. Misra, Y. Kong, and R. Kopperman, editors, Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine, volume 806 of Annals of the New York Academy of Sciences, pages 214-230, 1996.
14. A. Jung and R. Tix. The troublesome probabilistic powerdomain. In A. Edalat, A. Jung, K. Keimel, and M. Kwiatkowska, editors, Proceedings of the Third Workshop on Computation and Approximation, volume 13 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 1998. 23 pages.
15. A. Jung. Cartesian Closed Categories of Domains, volume 66 of CWI Tracts. Centrum voor Wiskunde en Informatica, Amsterdam, 1989. 107 pp.
16. A. Jung. The classification of continuous domains. In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 35-40. IEEE Computer Society Press, 1990.
17. Mathias Kegelmann. Continuous Domains in Logical Form, volume 49 of Electronic Notes in Theoretical Computer Science. Elsevier Science Publishers B.V., 2002.
18. O. Kirch. Bereiche und Bewertungen. Master's thesis, Technische Hochschule Darmstadt, June 1993. 77pp.
19. J. D. Lawson. The versatile continuous order. In M. Main, A. Melton, M. Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Language Semantics, volume 298 of Lecture Notes in Computer Science, pages 134-160. Springer Verlag, 1988.
20. J. D. Lawson. Domains, integration, and "positive analysis". Mathematical Structures in Computer Science, to appear.
21. M. A. Moshier and A. Jung. A logic for probabilities in semantics. In Julian Bradfield, editor, Computer Science Logic, volume 2471 of Lecture. Notes in Computer Science, pages 216-231. Springer Verlag, 2002.
22. M. A. Moshier. On the relationship between compact regularity and Gentzen's cut rule. Theoretical Computer Science, to appear.
23. L. Nachbin. Topology and Order. Von Nostrand, Princeton, N.J., 1965.
24. Translated from the 1950 monograph "Topologia e Ordem" (in Portugese). Reprinted by Robert E. Kreiger Publishing Co., Huntington, NY, 1967.
25. G. D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5:452-487, 1976.
26. G. D. Plotkin. Post-graduate lecture notes in advanced domain theory (incorporating the "Pisa Notes"). Dept. of Computer Science, Univ. of Edinburgh, 1981.
27. N. Saheb-Djahromi. CPO's of measures for nondeterminism. Theoretical Computer Science, 12:19-37, 1980.
28. R. Tix. Stetige Bewertungen auf topologischen Räumen. Master's thesis, Technische Hochschule Darmstadt, June 1995. 51pp.