Computing Dictionary
continuous function definition
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
(1994-11-30)