A function f : D -> E, where D and E are ref="module.php?name=Lexikon&file=search&eid=1&query=cpo">cpos, is continuous if it is ref="module.php?name=Lexikon&file=search&eid=1&query=monotonic">monotonic and f (lub Z) = lub ref="module.php?name=Lexikon&file=search&eid=1&query= f z | z in Z "> f z | z in Z for all ref="module.php?name=Lexikon&file=search&eid=1&query=directed">directed sets Z in D. In other words, the image of the lub is the lub of any directed image. All ref="module.php?name=Lexikon&file=search&eid=1&query=additive">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 ref="module.php?name=Lexikon&file=search&eid=1&query=least fixed point">least fixed point is fix f = lub ref="module.php?name=Lexikon&file=search&eid=1&query=f^n bottom | n = 0..infinity">f^n bottom | n = 0..infinity (1994-11-30)

In addition suitable contents:
[ ref="module.php?name=Lexikon&op=content&tid=134">= ] [ ref="module.php?name=Lexikon&op=content&tid=262">ad ] [ ref="module.php?name=Lexikon&op=content&tid=302">additive ] [ ref="module.php?name=Lexikon&op=content&tid=396">ag ] [ ref="module.php?name=Lexikon&op=content&tid=411">ai ] [ ref="module.php?name=Lexikon&op=content&tid=433">al ] [ ref="module.php?name=Lexikon&op=content&tid=544">am ] [ ref="module.php?name=Lexikon&op=content&tid=592">an ] [ ref="module.php?name=Lexikon&op=content&tid=740">ar ] [ ref="module.php?name=Lexikon&op=content&tid=743">arc ] [ ref="module.php?name=Lexikon&op=content&tid=800">as ] [ ref="module.php?name=Lexikon&op=content&tid=1026">b ] [ ref="module.php?name=Lexikon&op=content&tid=1444">bo ] [ ref="module.php?name=Lexikon&op=content&tid=1501">bot ] [ ref="module.php?name=Lexikon&op=content&tid=1503">bottom ] [ ref="module.php?name=Lexikon&op=content&tid=1606">bs ] [ ref="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ref="module.php?name=Lexikon&op=content&tid=2247">co ] [ ref="module.php?name=Lexikon&op=content&tid=2545">con ] [ ref="module.php?name=Lexikon&op=content&tid=2777">cpo ] [ ref="module.php?name=Lexikon&op=content&tid=2976">D ] [ ref="module.php?name=Lexikon&op=content&tid=3136">dd ] [ ref="module.php?name=Lexikon&op=content&tid=3151">de ] [ ref="module.php?name=Lexikon&op=content&tid=3436">ding ] [ ref="module.php?name=Lexikon&op=content&tid=3565">do ] [ ref="module.php?name=Lexikon&op=content&tid=3595">domain ] [ ref="module.php?name=Lexikon&op=content&tid=3752">du ] [ ref="module.php?name=Lexikon&op=content&tid=3834">E ] [ ref="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ref="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ref="module.php?name=Lexikon&op=content&tid=4008">element ] [ ref="module.php?name=Lexikon&op=content&tid=4148">er ] [ ref="module.php?name=Lexikon&op=content&tid=4171">es ] [ ref="module.php?name=Lexikon&op=content&tid=4199">et ] [ ref="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ref="module.php?name=Lexikon&op=content&tid=4520">file ] [ ref="module.php?name=Lexikon&op=content&tid=4595">fix ] [ ref="module.php?name=Lexikon&op=content&tid=4597">fixed point ] [ ref="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ref="module.php?name=Lexikon&op=content&tid=4727">for ] [ ref="module.php?name=Lexikon&op=content&tid=4940">function ] [ ref="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ref="module.php?name=Lexikon&op=content&tid=5434">h ] [ ref="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ref="module.php?name=Lexikon&op=content&tid=5931">id ] [ ref="module.php?name=Lexikon&op=content&tid=6013">il ] [ ref="module.php?name=Lexikon&op=content&tid=6024">image ] [ ref="module.php?name=Lexikon&op=content&tid=6064">in ] [ ref="module.php?name=Lexikon&op=content&tid=6108">infinity ] [ ref="module.php?name=Lexikon&op=content&tid=6194">int ] [ ref="module.php?name=Lexikon&op=content&tid=6413">io ] [ ref="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ref="module.php?name=Lexikon&op=content&tid=6482">is ] [ ref="module.php?name=Lexikon&op=content&tid=6558">it ] [ ref="module.php?name=Lexikon&op=content&tid=7045">least fixed point ] [ ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ref="module.php?name=Lexikon&op=content&tid=7417">lub ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8096">monotonic ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ref="module.php?name=Lexikon&op=content&tid=8622">nf ] [ ref="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ref="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ref="module.php?name=Lexikon&op=content&tid=8675">no ] [ ref="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ref="module.php?name=Lexikon&op=content&tid=8787">nu ] [ ref="module.php?name=Lexikon&op=content&tid=8964">om ] [ ref="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ref="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ref="module.php?name=Lexikon&op=content&tid=9762">point ] [ ref="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ref="module.php?name=Lexikon&op=content&tid=10253">query ] [ ref="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ref="module.php?name=Lexikon&op=content&tid=10385">re ] [ ref="module.php?name=Lexikon&op=content&tid=11150">se ] [ ref="module.php?name=Lexikon&op=content&tid=11259">serve ] [ ref="module.php?name=Lexikon&op=content&tid=11281">set ] [ ref="module.php?name=Lexikon&op=content&tid=11934">st ] [ ref="module.php?name=Lexikon&op=content&tid=12359">T ] [ ref="module.php?name=Lexikon&op=content&tid=12588">th ] [ ref="module.php?name=Lexikon&op=content&tid=12721">to ] [ ref="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ref="module.php?name=Lexikon&op=content&tid=13175">us ] [ ref="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ref="module.php?name=Lexikon&op=content&tid=13820">word ] [ ref="module.php?name=Lexikon&op=content&tid=14079">Z ]