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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0674106-5
PII: S 0002-9939(1982)0674106-5
Article copyright: © Copyright 1982 American Mathematical Society