Lattices of continuous monotonic functions

Miriam Cohen, Matatyahu Rubin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Let Y 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 〈X.I〉 has the Tietze extension property for order preserving continuous functions from X to I. Denote by M(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.

Original languageEnglish
Pages (from-to)685-691
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - 1 Jan 1982

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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