\(\alpha\)-Specker spaces (Q1398191)

A topological space \(X\) is called a Specker space if it has a clopen \(\pi\)-base and each continuous real-valued function on \(X\) is locally constant on a dense open set. In this paper, the authors consider various modifications of the notion of Specker space, and establish relationships between them using techniques from the theory of Archimedean \(\ell\)-groups.