Abstract
The Tarski fixed point theorem, concerning an isotone mapping of a partially ordered set into itself, is extended to mappings which are not necessarily isotone, but which must map a totally ordered set into itself. The key requirement is that the function be continuous (in a certain sense) whenever it is “decreasing". Then a ≦ f ( a ) , f ( b ) ≦ b a \leqq f(a),f(b) \leqq b , and a ≦ b ⇒ a \leqq b \Rightarrow the existence of a fixed point of f f .
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