Decomposition of function-lattices
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- Proc. Amer. Math. Soc. 28 (1971), 189-190 Request permission
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
- Robert L. Blair and Claude W. Burrill, Direct decompositions of lattices of continuous functions, Proc. Amer. Math. Soc. 13 (1962), 631–634. MR 139000, DOI 10.1090/S0002-9939-1962-0139000-4
- Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 20715, DOI 10.1090/S0002-9904-1947-08856-X
Additional Information
- © Copyright 1971 American Mathematical Society
- 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