Definition:Jointly Scott Continuous

Definition
Let $\left({S, \preceq}\right)$ 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 $\left({S, \preceq, \tau}\right)$
 * for every topological space $T = \left({S, \tau}\right)$: $f$ is continuous as a mapping from $T \times T$ into $T$.

where $T \times T$ denotes the product topology.