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Martin Sleziak
Martin Sleziak
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One of the most awesome fixed-point theorems I know of is due to PataraiaPataraia:

  • If $L$ is a poset with a bottom element and with joins of directed subsets, then every monotone function $f: L \to L$ has a (least) fixed point.

It is a strengthening of the Knaster-Tarski theorem, and is somewhat reminiscent of the Bourbaki-Witt theoremBourbaki-Witt theorem, but is entirely constructive. Related discussion at the n-Category Café herehere.

One of the most awesome fixed-point theorems I know of is due to Pataraia:

  • If $L$ is a poset with a bottom element and with joins of directed subsets, then every monotone function $f: L \to L$ has a (least) fixed point.

It is a strengthening of the Knaster-Tarski theorem, and is somewhat reminiscent of the Bourbaki-Witt theorem, but is entirely constructive. Related discussion at the n-Category Café here.

One of the most awesome fixed-point theorems I know of is due to Pataraia:

  • If $L$ is a poset with a bottom element and with joins of directed subsets, then every monotone function $f: L \to L$ has a (least) fixed point.

It is a strengthening of the Knaster-Tarski theorem, and is somewhat reminiscent of the Bourbaki-Witt theorem, but is entirely constructive. Related discussion at the n-Category Café here.

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Todd Trimble
Todd Trimble
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One of the most awesome fixed-point theorems I know of is due to Pataraia:

  • If $L$ is a poset with a bottom element and with joins of directed subsets, then every monotone function $f: L \to L$ has a (least) fixed point.

It is a strengthening of the Knaster-Tarski theorem, and is somewhat reminiscent of the Bourbaki-Witt theorem, but is entirely constructive. Related discussion at the n-Category Café here.