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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 797–806 | Cite as

The Spectral Theory of Semitopological Semilattices

  • Yu. L. Ershov
Article

Abstract

We characterize the spaces SpecS of prime closed ideals of an arbitrary semitopological semilattice S. We give an abstract description for the natural homomorphism of such a semilattice S into the semilattice <T*,∪> of the topology T* of the space SpecS

semilattice semitopological semilattice prime ideal prime filter distributive semilattice 

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References

  1. 1.
    Grätzer G., General Lattice Theory [Russian translation], Mir, Moscow (1982).Google Scholar
  2. 2.
    Gierz G., Hofmann K. H., Keimel K., Lawson J. D., Mislove M., and Scott D., A Compendium of Continuous Lattices, Springer-Verlag, Berlin; Heidelberg; New York (1980).Google Scholar
  3. 3.
    Hofmann K. H. and Keimel K. A General Character Theory for Partially Ordered Sets and Lattices, Amer. Math. Soc., Providence (1972). (Mem. Amer. Math. Soc.; 122.)Google Scholar
  4. 4.
    Hofmann K. H., Mislove M., and Stralka A., The Pontryagin Duality of Compact 0-Dimensional Semilattices and Its Applications, Springer-Verlag, Berlin; Heidelberg; New York (1974). (Lecture Notes in Math.; 396.)Google Scholar
  5. 5.
    Day B. J. and Kelly G. M., “On topological quotient maps preserved by pull-backs on products,” Proc. Cambridge Philos. Soc., 67, 553–558 (1970).Google Scholar
  6. 6.
    Ershov Yu. L., “On essential extensions of T0-spaces,” Dokl. Ros. Akad. Nauk, 368, No. 3, 299–302 (1999).Google Scholar
  7. 7.
    Ershov Yu. L., The Theory of Enumerations [in Russian], Nauka, Moscow (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Yu. L. Ershov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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