Definition:Jointly Scott Continuous

Definition
Let $\struct{S, \preceq}$ be an ordered set.

Let $f:S \times S \to S$ be a mapping.

$f$ is jointly Scott continuous
 * 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.