continuous function
<mathematics >
A function f : D -> E, where D and E are cpos, is continuous if it is monotonic and
f (lub Z) = lub { f z | z in Z }
for all directed sets Z in D. In other words, the image of
the lub is the lub of any directed image.
All additive functions (functions which preserve all lubs)
are continuous. A continuous function has a least fixed
point if its domain has a least element, bottom (i.e. it
is a cpo or a "pointed cpo" depending on your definition of a
cpo). The least fixed point is
fix f = lub {f^n bottom | n = 0..infinity}
Last updated: 1994年11月30日
Nearby terms:
continuations ♦ continuous function ♦ Continuous System Modeling Program
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