Skip to main content
SpringerLink
Log in

Catalytic distributive lattices and compact zero-dimensional topological lattices

  • Published:
algebra universalis Aims and scope Submit manuscript

Abstract

The (Priestley) dual spaces ofD 01-catalytic lattices are analysed and shown to be precisely the compact zero-dimensional topological lattices. This characterisation is used to prove that a bounded distributive lattice isD 01-catalytic if and only if it is a retract of one freely generated by an ordered set.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. E. Adams,The poset of prime ideals of a distributive lattice, Algebra Univ. 5 (1975), 141–142.

    Google Scholar 

  2. R. Balbes,On the partially ordered set of prime ideals of a distributive lattice, Canad. J. Math.23 (1971), 866–874.

    Google Scholar 

  3. R. Balbes,Catalytic distributive lattices, Algebra Univ.11 (1980), 334–340.

    Google Scholar 

  4. B. A. Davey,A note on representable posets, Algebra Univ.3 (1973), 345–347.

    Google Scholar 

  5. B. A. Davey,On the lattice of subvarieties, Houston J. Math.5 (1979), 183–192.

    Google Scholar 

  6. B. A. Davey andI. Rival,Exponents of lattice-ordered algebras, Algebra Univ.14 (1982), 87–98.

    Google Scholar 

  7. M. Erne,Separation axioms for interval topologies, Proc. Amer. Math. Soc.79 (1980), 185–190.

    Google Scholar 

  8. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove andD. S. Scott,A compendium of continuous lattices, Springer-Verlag, Berlin, Heidelberg, New York (1980).

    Google Scholar 

  9. G. Gierz andJ. D. Lawson,Generalized continuous and hypercontinuous lattices, Rocky Mountain J. Math.11 (1981), 271–296.

    Google Scholar 

  10. T. G. Kucera andB. Sands,Lattices of lattice homomorphisms, Algebra Univ.8 (1978), 180–190.

    Google Scholar 

  11. H. A. Priestley,Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc.2 (1970), 186–190.

    Google Scholar 

  12. G. N. Raney,Tight Galois connections and complete distributivity, Trans. Amer. Math. Soc. 97 (1960), 418–426.

    Google Scholar 

  13. T.Tan,On representable posets, Ph.D. thesis, University of Manitoba (1974).

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute St. Giles, Oxford, England

    H. A. Priestley

Authors
  1. H. A. Priestley
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Priestley, H.A. Catalytic distributive lattices and compact zero-dimensional topological lattices. Algebra Universalis 19, 322–329 (1984). https://doi.org/10.1007/BF01201099

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01201099

Keywords

Search

Navigation