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Lattices of Continuous Monotonic Functions

1982
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Proceedings of the American Mathematical Society
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Let Y 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 (X.I) has the Tietze extension property for order preserving continuous functions from X to /. Denote by M( X, !) the lattice of order preserving continuous functions from X to /. We generalize a theorem of Kaplanski [K], and show that as a lattice alone, M( X, I) characterizes X as an

doi:10.2307/2043610
fatcat:qdqdbyskqnhwvonyljpalwrtei