Proving open properties by induction
The author defines a concept of noetherian induction, which generalizes strong induction for natural numbers and transfinite induction, and, in a certain sense, is shown to be the most general type of induction. He also shows that in a complete partial order (every nonempty chain has a least upper bound) for a property which is inductive and open, the set of elements satisfying it is open in the lower topology (in which subsets are closed if they contain the least upper bound of their directed subsets).
scientific article; zbMATH DE number 4079422