Lattices of continuous monotonic functions
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- by Miriam Cohen and Matatyahu Rubin PDF
- Proc. Amer. Math. Soc. 86 (1982), 685-691 Request permission
Abstract:
Let $X$ be a compact Hausdorff space equipped with a closed partial ordering. Let $I$ be a linear ordering that either does not have a maximal element or does not have a minimal element. We further assume that $\langle {X,I} \rangle$ has the Tietze extension property for order preserving continuous functions from $X$ to $I$. Denote by $(X,I)$ the lattice of order preserving continuous functions from $X$ to $I$. We generalize a theorem of Kaplanski [K], and show that as a lattice alone, $M(X,I)$ characterizes $X$ as an ordered space.References
- Irving Kaplansky, Lattices of continuous functions, Bull. Amer. Math. Soc. 53 (1947), 617–623. MR 20715, DOI 10.1090/S0002-9904-1947-08856-X
- Leopoldo Nachbin, Topology and order, Van Nostrand Mathematical Studies, No. 4, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. Translated from the Portuguese by Lulu Bechtolsheim. MR 0219042
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 685-691
- MSC: Primary 54F05; Secondary 54C20, 54C35
- DOI: https://doi.org/10.1090/S0002-9939-1982-0674106-5
- MathSciNet review: 674106