Summary
In this paper without using any of the equivalent statements of the Axiom of Choice we give a short proof of the Fixed Point Theorems 1 and 2, and, via a simple derivation of Zorn’s Lemma from the Axiom of Choice (see Theorem 3) we prove Fixed Point Theorem 4.
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Abian, A. Fixed point theorems of the mappings of partially ordered sets. Rend. Circ. Mat. Palermo 20, 139–142 (1971). https://doi.org/10.1007/BF02844167
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DOI: https://doi.org/10.1007/BF02844167