Banach and Knaster-Tarski fixed point theorems -- are they related? - MathOverflow

Banach and Knaster-Tarski fixed point theorems -- are they related?

2010-08-04T15:04:59Z

It there any known way of obtaining the Banach fixed-point theorem from the Tarski fixed-point theorem or vice-versa?

Answer by Matteo Mio for Banach and Knaster-Tarski fixed point theorems -- are they related?

2011-01-24T10:16:19Z

Hello,

I just found the question, so the answer might come a bit too lat, but.. Have a look at:

Paweł Waszkiewicz, "Common patterns for metric and ordered fixed point theorems.", In Proceedings of the 7th Workshop on Fixed Points in Computer Science (Luigi Santocanale ed.), 2010, pp. 83-87.

I attended this talk last summer, and it addresses exactly your question.

Answer by Driss Misane for Banach and Knaster-Tarski fixed point theorems -- are they related?

2012-02-20T08:31:13Z

Look the article : M.Jawahiri, D. Misane, M. Pouzet. Retracts: graphs and ordrerd sets from the metric point of view. Contemporary Mathematics, 1986, vol. 57 pp. 175-226

Answer by Michał Kukieła for Banach and Knaster-Tarski fixed point theorems -- are they related?

2012-05-15T12:11:57Z

As suggested by Jacques, I turn my comment into an answer.

This is not exactly what you ask for, but it is related. Efe Ok in Section 3.4 in Chapter 6 of his yet-to-be-written book on ordered sets gives a proof of the Banach fixed point theorem using the Kantorovitch-Tarski fixed point theorem: files.nyu.edu/eo1/public/Book-PDF/CHAPTER%205.pdf