Generalization To Partial Orders: Prefixpoint and Postfixpoint
The notion and terminology is generalized to a partial order. Let ≤ be a partial order over a set X and let f:X → X be a function over X. Then a prefixpoint (also spelled pre-fixpoint) of f is any p such that f(p) ≤ p. Analogously a postfixpoint (or post-fixpoint) of f is any p such that p ≤ f(p). One way to express the Knaster–Tarski theorem is to say that a monotone function on a complete lattice has a least fixpoint which coincides with its least prefixpoint (and similarly its greatest fixpoint coincides with its greatest postfixpoint). Prefixpoints and postfixpoints have applications in theoretical computer science.
Read more about this topic: Fixed Point (mathematics)
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