In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed-point theorem for partially ordered sets. It states that if X is a non-empty poset that is chain complete, meaning each chain has a least upper bound, and f : X → X {\displaystyle f:X\to X} is a function such that f ( x ) ≥ x {\displaystyle f(x)\geq x} for all x , {\displaystyle x,} then f {\displaystyle f} has a fixed point.
In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed-point theorem for partially ordered sets. It states that if X is a non-empty poset that is chain complete, meaning each chain has a least upper bound, and f : X → X {\displaystyle f:X\to X} is a function such that f ( x ) ≥ x {\displaystyle f(x)\geq x} for all x , {\displaystyle x,} then f {\displaystyle f} has a fixed point.
Source: Wikipedia "Bourbaki–Witt theorem" · CC BY-SA 4.0
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