Equational theory of continuous lattices (Q805642)

There are standard equational characterizations of continuous lattices among the complete lattices; the equations in question involve a certain general infinitary distributive law. The author characterizes continuous lattices as posets equipped with an infinitary operation of ``inf'' for each cardinal and a P-ary operation of ``lim inf'' for each directed poset P, for which these operations satisfy a small number of very natural equations. These operations and laws are all algebraic in that they are preserved by morphisms of continuous lattices.