continuous function
A function f : D -> E, where D and E are {cpo}s, 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}
(1994-11-30)