\begin{definition}[Definition:Jointly Scott Continuous]
Let $\struct{S, \preceq}$ be an ordered set.
Let $f:S \times S \to S$ be a mapping.
$f$ is '''jointly Scott continuous''' {{iff}}
:for every relational structure with Scott topology $\struct{S, \preceq, \tau}$
:for every topological space $T = \struct{S, \tau}$: $f$ is continuous as a mapping from $T \times T$ into $T$.
where $T \times T$ denotes the product space.
{{NamedforDef|Dana Stewart Scott|cat = Scott, Dana}}
\end{definition}