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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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.


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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