Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T18:01:11.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Metrizability Conditions for Completely Distributive Lattices

Published online by Cambridge University Press:  20 November 2018

G. Gierz ,
J. D. Lawson  and
A. R. Stralka
G. Gierz
Affiliation:
University of California at Riverside, California 92521
J. D. Lawson
Affiliation:
University of California at Riverside, California 92521
A. R. Stralka
Affiliation:
Louisana State University, Baton RougeLA, 70808
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A lattice is said to be essentially metrizable if it is an essential extension of a countable lattice. The main result of this paper is that for a completely distributive lattice the following conditions are equivalent: (1) the interval topology on L is metrizable, (2) L is essentially metrizable, (3) L has a doubly ordergenerating sublattice, (4) L is an essential extension of a countable chain.

Keywords

06D1006B3054H12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 446 - 453
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Banaschewski, B. and Bruns, G., Injective hulls in the category of distributive lattices, J. reine u. angewandte Math. 232 (1968), 102-109.Google Scholar
2. Clinkenbeard, D. J., The lattice of closed congruences on a topological lattice. Trans. Amer. Math. Soc. 263 (1981), 457-467.Google Scholar
3. Floyd, E. E., Boolean algebras with pathological order topologies, Pacific J. Math 5 (1955), 687-689.Google Scholar
4. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D. S., A Compendium of Continuous Lattices, Springer-Verlag, Heidelberg, 1980.Google Scholar
5. Hofmann, K. H. and Mostert, P. S., Elements of Compact Semi-groups, Merrill Publ. Co., Columbus, Ohio, 1966.Google Scholar
6. Papert-Strauss, D., Topological lattices, Proc. London Math. Soc. 18 (1968), 217-230.Google Scholar