Ordering a square (Q2352123)

A linear ordered set \(X\) with the topology having a subbase of open rays is a linearly ordered topological space, or a LOTS. Any subspace of a LOTS is a generalized ordered space, or a GO-space. If \(X\) is not discrete, let \(\tau\) be the largest cardinal number such that the intersection of any fewer than \(\tau\) open subsets of \(X\) is open. If \(X\) has a \(\tau\)-discrete basis of clopen sets, the author shows that \(X^n\) is a GO-space for any \(n \in \mathbb{N}\). Several related results are given and the paper closes with open questions about spaces \(X\) for which \(X \times X\) is a LOTS or a GO-space.