The duality between lattice-ordered monoids and ordered topological spaces (Q1080225)

The authors show that a realcompact ordered space X can be characterized by the lattice-ordered convergence monoid \(C(X,{\mathbb{R}}^+)\) of continuous isotone functions on X to the non-negative reals \({\mathbb{R}}^+\), and that a zero-dimensionally realcompact ordered space X can be determined by the lattice-ordered convergence monoid C(X,\({\mathbb{N}})\) of continuous isotone functions on X to the natural numbers \({\mathbb{N}}\) if the order is discrete, chain or Dedekind complete.