Meaning of CONTINUOUS FUNCTION in English
- 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
FOLDOC computer English dictionary. Английский словарь по компьютерам FOLDOC. 2012