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
- 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices
- Mizar article WAYBEL14:def 1