; TeX output 2003.08.11:2237 C Ghtml: html: Gz html: html:4 ?~Dt G G cmr17An7tAlgebraicApproacqhtoStableDomains /cXQ cmr12PraulTVaylor +written1988,published1991#R U*t: cmbx9Abstracth&)o cmr9Da9yyP[75]showedthatthecategoryofconCtinuous&latticesyPandmapswhichpreserve directedjoinsand+j cmti9arbitraryoLmeetsisthecategoryofalgebrasforamonado9verSet,Sp<`or PCos),Jthe@(freefunctorbAeingthesetofltersofopensets.Separately:,JBerry[78]constructed a:cartesianclosedcategorywhosemorphismspreserv9edirectedjoinsandconnectedWmeets, whilst(Diers[79]consideredsimilarfunctorsindepAenden9tlyinastudyofcategoriesofmodels ofdisjunctivCestheories.uGirard[85]builtonBerry'sw9orktobuildanewandverylean moAdelTofpKolymorphism.&In thispapAerw9ebringthesestrandstogether,deningamonadbasedonltersu5ofcon- nectedopKensetsandsho9wingthatitscategoryofalgebrashasBerry's(stable)morphisms and4iscartesianclosed.z;Theob jectsha9ve4mCultijoinsasinDiers'w9ork,