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Proceedings of the American Mathematical Society

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Complete lattices and the generalized Cantor theorem


Authors: Roy O. Davies, Allan Hayes and George Rousseau
Journal: Proc. Amer. Math. Soc. 27 (1971), 253-258
MSC: Primary 06.30
DOI: https://doi.org/10.1090/S0002-9939-1971-0268091-0
MathSciNet review: 0268091
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Abstract: Cantor's Theorem is generalized to a theorem on partially ordered sets.


References [Enhancements On Off] (What's this?)

  • [1] A. C. Davis, A characterization of complete lattices, Pacific J. Math. 5 (1955), 311-319. MR 17, 574. MR 0074377 (17:574e)
  • [2] A. M. Gleason and R. P. Dilworth, A generalized Cantor theorem, Proc. Amer. Math. Soc. 13 (1962), 704-705. MR 26 #2365. MR 0144824 (26:2365)
  • [3] W. Sierpiński, Sur un problème concernant les sous-ensembles croissants du continu, Fund. Math. 3 (1922), 109-112.
  • [4] A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285-309. MR 17, 574. MR 0074376 (17:574d)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0268091-0
Keywords: Cantor's Theorem, left continuity, monotone mappings
Article copyright: © Copyright 1971 American Mathematical Society

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