Abstract
We introduce the concept of quasi–hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi–hyperalgebraic. Some characterizations of quasi–hyperalgebraic lattices are presented. We also prove that the Smyth powerdomain of a quasi–hyperalgebraic lattice is hyperalgebraic.
Similar content being viewed by others
References
Priestley, H. A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc., 2, 186–190 (1970)
Venugopalan, P.: Priestley spaces. Proceedings of the American Mathematics Society, 109(3), 605–610 (1990)
Flagg, B.: Algebraic theories of compact pospaces. Topology and Its Applications, 77, 277–290 (1997)
Lawson, J. D.: The upper interval topology, Property M, and compactness, Electronic Notes in Theoretical Computer Science, 1998
Xu, X. Q., Liu, Y. M.: The Scott topology and Lawson topology on a Z–quasicontinuous domain (in Chinese). Chin. Ann. of Math., 24A(3), 365–376 (2003)
Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., Scott, D.: Continuous lattices and domains, Cambridge University Press, 2003
Heckmann, R.: Power Domain Constructions, PhD thesis, University des Saarlandes, 1990
Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., Scott, D.: A compendium of continuous lattices, Springer–Verlag, Berlin, 1980
Xu, X. Q., Liu, Y. M.: Regular relations and strictly completely regular ordered spaces. Topology and Its Applications, 135, 1–12 (2004)
Keimel, K., Paseka, J.: A direct proof of Hofmann–Mislove theorem. Proceedings of the American Mathematics Society, 120, 301–303 (1994)
Smyth, M.: Power domains. Journal of Computer and System Sciences, 16, 23–36 (1978)
Gierz, G., Lawson, J. D.: Generalized continuous and hypercontinuous lattices. Rocky Mountain J. Math., 11, 271–296 (1981)
Heckmann, R.: An upper power domain construction in terms of strongly compact sets, Lecture Notes in Computer Science, Springer–Verlag, New York, 598, 272–293, 1992
Xu, X. Q., Luo, M. K., Huang, Y.: Quasi Z–continuous domains and Z–meet continuous domains. Acta Mathematica Sinica, Chinese Series, 48A(2), 221–234 (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NSFC(10331010) and Research Fund for the Doctoral Program of Higher Education
Rights and permissions
About this article
Cite this article
Yang, J.B., Luo, M.K. Priestley Spaces, Quasi–hyperalgebraic Lattices and Smyth Powerdomains. Acta Math Sinica 22, 951–958 (2006). https://doi.org/10.1007/s10114-005-0737-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-005-0737-8
Keywords
- Priestley space
- quasi–hyperalgebraic lattice
- hypercontinuous lattice
- hyperalgebraic lattice
- Smyth powerdomain