Kleene fixed-point theorem

In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following: Kleene Fixed-Point Theorem. Suppose ( L , ⊑ ) {\displaystyle (L,\sqsubseteq )} is a directed-complete partial order (dcpo) with a least element, and let f : L → L {\displaystyle f:L\to L} be a Scott-continuous (and therefore monotone) function.

Source: Wikipedia — Kleene fixed-point theorem (CC BY-SA 4.0)