\begin{definition}[Definition:Complete Order Topology]
Let $\struct {S, \preceq}$ be a complete ordered set.
Let $\tau$ be the order topology on $\struct {S, \preceq}$.
Then $\tau$ is a '''complete order topology'''.
Hence $\struct {S, \preceq, \tau}$ is a '''complete order space'''.
\end{definition}