Decomposition of function-lattices
Abstract: We give a simple direct proof of the theorem (due to Kaplansky-Blair-Burrill) that the lattice of all continuous functions defined on the topological space with values in the chain can be decomposed iff contains an open-and-closed subset.
-  Robert L. Blair and Claude W. Burrill, Direct decompositions of lattices of continuous functions, Proc. Amer. Math. Soc. 13 (1962), 631–634. MR 0139000, https://doi.org/10.1090/S0002-9939-1962-0139000-4
-  Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 0020715, https://doi.org/10.1090/S0002-9904-1947-08856-X
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Keywords: Lattices of chain-valued functions, adequate sublattices, homomorphism, connectedness
Article copyright: © Copyright 1971 American Mathematical Society