Scott topology derived from this order is finer than the original topology. 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 dcpo's, two particularly notable examples of Scott-continuous functions are curry and apply. Nuel Belnap used Scott continuity to extend logical connectives to a four-valued logic. See also Alexandrov topology Upper topology Footnotes References Order theory General topology Domain theory