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Fixed point theorems in metric and uniform spaces via the Knaster-Tarski Principle
Nonlinear Analysis: Theory, Methods & Applications, 1998The proofs of many fixed point theorems in metric partially ordered sets are based on Bourbaki-Kneser and Knaster-Tarski principles. The author emphasizes that both these theorems are independent of the axiom of choice and notices that proofs of them are almost immediate, if one uses Zorn's lemma.
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Some issues concerning fixed points in computational logic: Quasi-metrics, multivalued mappings and the Knaster-Tarski theorem [PDF]
, 1999 Summary: Many questions concerning the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. We discuss known versions, for multivalued mappings, of the Knaster-Tarski theorem and of the Banach contraction mapping theorem, and ...
Hitzler, Pascal, Seda, Anthony K.
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