Further Results
Besides the previous representation results, there are some other statements that can be made about complete lattices, or that take a particularly simple form in this case. An example is the Knaster–Tarski theorem, which states that the set of fixed points of a monotone function on a complete lattice is again a complete lattice. This is easily seen to be a generalization of the above observation about the images of closure operators, since these are exactly the sets of fixed points of such operators.
Read more about this topic: Complete Lattice
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