additive

<mathematics>

A function f : X -> Y is additive if

 for all Z <= X
 f (lub Z)  =  lub { f z : z in Z }

(f "preserves lubs"). All additive functions defined over cpos are continuous.

("<=" is written in LaTeX as \subseteq, "lub" as \sqcup ).

Last updated: 1995-02-03

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