CONTINUOUS FUNCTION
\kəntˈɪnjuːəs fˈʌŋkʃən], \kəntˈɪnjuːəs fˈʌŋkʃən], \k_ə_n_t_ˈɪ_n_j_uː_ə_s f_ˈʌ_ŋ_k_ʃ_ə_n]\
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A function f : D > E, where D and E are cpos, is continuousif it is monotonic andf (lub Z) = lub f z  z in Z for all directed sets Z in D. In other words, the image ofthe lub is the lub of any directed image.All additive functions (functions which preserve all lubs)are continuous. A continuous function has a least fixedpoint if its domain has a least element, bottom (i.e. itis a cpo or a "pointed cpo" depending on your definition of acpo). The least fixed point isfix f = lub f^n bottom  n = 0..infinity
By Denis Howe
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