Priestley spaces

Author:
P. Venugopalan

Journal:
Proc. Amer. Math. Soc. **109** (1990), 605-610

MSC:
Primary 06B35; Secondary 06B30, 54F05

MathSciNet review:
1013985

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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.

**[1]**Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, and Dana S. Scott,*A compendium of continuous lattices*, Springer-Verlag, Berlin-New York, 1980. MR**614752****[2]**G. Gierz and J. D. Lawson,*Generalized continuous and hypercontinuous lattices*, Rocky Mountain J. Math.**11**(1981), no. 2, 271–296. MR**619676**, 10.1216/RMJ-1981-11-2-271**[3]**G. Gierz, J. D. Lawson, and A. Stralka,*Quasicontinuous posets*, Houston J. Math.**9**(1983), no. 2, 191–208. MR**703268****[4]**M. Hochster,*Prime ideal structure in commutative rings*, Trans. Amer. Math. Soc.**142**(1969), 43–60. MR**0251026**, 10.1090/S0002-9947-1969-0251026-X**[5]**H. A. Priestley,*Representation of distributive lattices by means of ordered stone spaces*, Bull. London Math. Soc.**2**(1970), 186–190. MR**0265242****[6]**H. A. Priestley,*Ordered topological spaces and the representation of distributive lattices*, Proc. London Math. Soc. (3)**24**(1972), 507–530. MR**0300949****[7]**Maurice Pouzet and Denis Richard (eds.),*Orders: description and roles*, North-Holland Mathematics Studies, vol. 99, North-Holland Publishing Co., Amsterdam, 1984. Annals of Discrete Mathematics, 23. MR**779841****[8]**Hilary A. Priestley,*Algebraic lattices as dual spaces of distributive lattices*, Continuous lattices and their applications (Bremen, 1982) Lecture Notes in Pure and Appl. Math., vol. 101, Dekker, New York, 1985, pp. 237–249. MR**826005****[9]**Albert Stralka,*A partially ordered space which is not a Priestley space*, Semigroup Forum**20**(1980), no. 4, 293–297. MR**583112**, 10.1007/BF02572690**[10]**P. Venugopalan,*Quasicontinuous posets*, Semigroup Forum**41**(1990), no. 2, 193–200. MR**1057590**, 10.1007/BF02573390**[11]**P. Venugopalan,*A generalization of completely distributive lattices*, Algebra Universalis**27**(1990), no. 4, 578–586. MR**1387903**, 10.1007/BF01189001

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1013985-3

Keywords:
Complete lattice,
Priestley space,
Lawson topology,
interval topology

Article copyright:
© Copyright 1990
American Mathematical Society