Examples
The open sets in a given topological space when ordered by inclusion form a lattice on which the Scott topology can be defined. A subset X of a topological space T is compact with respect to the topology on T (in the sense that every open cover of X contains a finite subcover of X) if and only if the set of open neighbourhoods of X is open with respect to the Scott topology.
For CPO, the cartesian closed category of complete partial orders, two particularly notable examples of Scott-continuous functions are curry and apply.
Read more about this topic: Scott Continuity
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