Algebraic theories of continuous lattices

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


Natural Transformation Compact Hausdorff Space Continuous Lattice Left Adjoint Forgetful Functor 
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  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

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