LOTS and GO spaces (Q1187247)

If \(\leq\) is a linear order on a set \(X\), then \(T(\leq)\) denotes the topology on \(X\) generated by all open intervals. A space \((X,T)\) is a KOTS (LOTS) provided that there is a linear order \(\leq\) on \(X\) such that \(T(\leq)\subset T\) \((T(\leq)=T)\). The main results are the following: Theorem 1. A connected LOTS is maximally connected and locally connected. -- Theorem 2. A connected and locally connected KOTS is a LOTS. A connected KOTS may fail to be a LOTS.