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Proceedings of the American Mathematical Society

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Decomposition of function-lattices


Author: S. D. Shore
Journal: Proc. Amer. Math. Soc. 28 (1971), 189-190
MSC: Primary 46.06
DOI: https://doi.org/10.1090/S0002-9939-1971-0271700-3
MathSciNet review: 0271700
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Abstract: We give a simple direct proof of the theorem (due to Kaplansky-Blair-Burrill) that the lattice $ C(X,K)$ of all continuous functions defined on the topological space $ X$ with values in the chain $ K$ can be decomposed iff $ X$ contains an open-and-closed subset.


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

  • [1] R. L. Blair and C. W. Burrill, Direct decompositions of lattices of continuous functions, Proc. Amer. Math. Soc. 13 (1962), 631-634. MR 25 #2440. MR 0139000 (25:2440)
  • [2] I. Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617-623. MR 8, 587. MR 0020715 (8:587e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271700-3
Keywords: Lattices of chain-valued functions, adequate sublattices, homomorphism, connectedness
Article copyright: © Copyright 1971 American Mathematical Society

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