Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Priestley spaces


Author: P. Venugopalan
Journal: Proc. Amer. Math. Soc. 109 (1990), 605-610
MSC: Primary 06B35; Secondary 06B30, 54F05
MathSciNet review: 1013985
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a purely order-theoretic characterization of complete lattices that are compact totally order-disconnected (Priestley) spaces with respect to the Lawson topology. We also characterize complete lattices that are Priestley spaces with respect to the interval topology.


References [Enhancements On Off] (What's this?)

  • [1] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, A compendium of continuous lattices, Springer-Verlag, Berlin, Heidelberg, and New York, 1980. MR 614752 (82h:06005)
  • [2] G. Gierz and J. D. Lawson, Generalized continuous and hypercontinuous lattices, Rocky Mountain J. Math. (1981), 271-296. MR 619676 (82h:54069)
  • [3] G. Gierz, J. D. Lawson, and A. Stralka, Quasicontinuous posets, Houston J. Math. 9 (1983), 191-208. MR 703268 (85b:06009)
  • [4] M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43-60. MR 0251026 (40:4257)
  • [5] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186-190. MR 0265242 (42:153)
  • [6] -, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 24 (1972), 507-530. MR 0300949 (46:109)
  • [7] -, Orders: description and roles (M. Pouzet and M. Richard, eds.), Annals of Discrete Math., North-Holland, Amsterdam, 1984, pp. 39-60. MR 779841 (85k:06001)
  • [8] H. A. Priestley, Algebraic lattices as duals of distributive lattices, Lecture Notes in Pure and Applied Math., vol. 101, 1985, pp. 237-249. MR 826005 (87i:06042)
  • [9] A. R. Stralka, A partially ordered space which is not a Priestley space, Semigroup Forum 20 (1980), 293-297. MR 583112 (82f:54051)
  • [10] P. Venugopalan, Quasicontinuous posets, Semigroup Forum (to appear). MR 1057590 (91i:06018)
  • [11] -, A generalization of completely distributive lattices, Algebra Universalis (to appear). MR 1387903 (97k:06019)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06B35, 06B30, 54F05

Retrieve articles in all journals with MSC: 06B35, 06B30, 54F05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013985-3
PII: S 0002-9939(1990)1013985-3
Keywords: Complete lattice, Priestley space, Lawson topology, interval topology
Article copyright: © Copyright 1990 American Mathematical Society