Lattices of continuous monotonic functions
Authors: Miriam Cohen and Matatyahu Rubin
Journal: Proc. Amer. Math. Soc. 86 (1982), 685-691
MSC: Primary 54F05; Secondary 54C20, 54C35
MathSciNet review: 674106
Abstract: Let be a compact Hausdorff space equipped with a closed partial ordering. Let be a linear ordering that either does not have a maximal element or does not have a minimal element. We further assume that has the Tietze extension property for order preserving continuous functions from to . Denote by the lattice of order preserving continuous functions from to . We generalize a theorem of Kaplanski [K], and show that as a lattice alone, characterizes as an ordered space.
- [K] 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
- [N] Leopoldo Nachbin, Topology and order, Translated from the Portuguese by Lulu Bechtolsheim. Van Nostrand Mathematical Studies, No. 4, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR 0219042