\begin{definition}[Definition:Scott Topology]
Let $\struct {S, \preceq}$ be an up-complete ordered set.
Let $T = \struct {S, \preceq, \tau}$ be a relational structure with topology.
Then $T$ has the '''Scott topology''' {{iff}}:
:$\tau$ is the set of all upper and inaccessible by directed suprema subsets of $S$.
\end{definition}