Ordered compactifications and families of maps (Q1363195)

Let \(X\) be an ordered space. A subset \(\Phi\) consisting of increasing, continuous functions from \(X\) into \([0,1]\) is a defining family if it induces both the weak order and weak topology on \(X\). For each such family the authors prove the existence of a smallest ordered compactification of \(X\) with the property that each member of \(\Phi\) can be extended over the compactification.