Definition:Jointly Scott Continuous

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Definition

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

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

$f$ is jointly Scott continuous if and only if

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.


Source of Name

This entry was named for Dana Stewart Scott.


Sources