Advertisement

Algebraic theories of continuous lattices

  • Oswald Wyler
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 871)

Keywords

Natural Transformation Compact Hausdorff Space Continuous Lattice Left Adjoint Forgetful Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Banaschewski. Essential extensions of T0 spaces. Gen. Topology Appl. 7:233–246, 1977.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Garrett Birkhoff. Lattice Theory, 3rd Ed. New York, 1967.Google Scholar
  3. [3]
    Alan Day. Filter monads, continuous lattices and closure systems. Canad. J. Math. 27:50–59, 1975.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Orrin Frink. Topology in lattices. Trans. A.M.S. 51:569–582, 1942.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Karl Heinrich Hofmann, Michael Mislove, Albert Stralka. The Pontryagin Duality of Compact 0 — dimensional Semilattices and its Applications. Lecture Notes in Math. 369, 1974.Google Scholar
  6. [6]
    Karl H. Hofmann and Albert Stralka. The algebraic theory of compact Lawson semilattices — applications of Galois connections to compact semilattices. Dissertationes Mathematicae 137, 1976. 54 pp.Google Scholar
  7. [7]
    K.H. Hofmann and O. Wyler. On the closedness of the set of primes in continuous lattices. SCS-Memo, 28 Dec. 1976.Google Scholar
  8. [8]
    H.-J. Kowalsky. Beiträge zur topologischen Algebra. Math. Nachrichten 11:143–185, 1954.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Jimmie D. Lawson. Vietoris Mappings and Embedding of Topological Semilattices. Phd Thesis, Univ. of Tennessee, 1967.Google Scholar
  10. [10]
    J.D. Lawson. Topological semilattices with small semilattices. J. London Math. Soc (2) 1:719–724, 1969.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    F.E.J. Linton. Coequalizers in categories of algebras. In Seminar on Triples and Categorical Homology Theory, pages 75–90. Lecture Notes in Math. 80, 1969.Google Scholar
  12. [12]
    Saunders MacLane. Categories for the Working Mathematician. Berlin, Heidelberg, New York, 1971.Google Scholar
  13. [13]
    E.G. Manes. A triple miscellany: Some aspects of the theory of algebras over a triple. PhD thesis, Wesleyan University, 1967.Google Scholar
  14. [14]
    E.G. Manes. Algebraic Theories. New York, Heidelberg, Berlin, 1976.Google Scholar
  15. [15]
    Marcus M. McWaters. A note on topological semilattices. J. London Math. Soc. (2) 1:64–66, 1969.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Ernest Michael. Topologies on spaces of subsets. Trans. A.M.S. 71:152–182, 1951.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Leopoldo Nachbin. Topology and Order. Princeton, 1965.Google Scholar
  18. [18]
    Dana Scott. Continuous lattices. In Toposes, Algebraic Geometry and Logic, pages 93–136. Lecture Notes in Math. 274, 1972.Google Scholar
  19. [19]
    Leopold Vietoris. Bereiche zweiter Ordnung. Monatsh. für Math. und Physik 32:258–280, 1922.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Leopold Vietoris. Kontinua zweiter Ordnung. Monatsh. für Math. und Physik 32:258–280, 1922.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Oswald Wyler. Algebraic theories of continuous lattices. Technical Report, Carnegie-Mellon University, December, 1976.Google Scholar
  22. [22]
    Oswald Wyler. On continuous lattices as topological algebras. Technical Report, Carnegie-Mellon University, March, 1977.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Oswald Wyler
    • 1
  1. 1.Department of MathematicsCarnegie - Mellon UniversityPittsburghUSA

Personalised recommendations