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Does anybody know the paper where the Brouwer fixed point theorem first appeared?

Wikipedia and other articles available online have no reference. Schauder's paper about his fixed point theorem is available online at

but, even if I don't speak a word of German, it seems to me that there is no reference.

In Brouwer's wikipage

there are some references to Brouwer's papers, but only focused on his contribution to philosophy and philosophy of math.

Thanks in advance,


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Sorry did misread the question;) – Marc Palm Mar 6 '12 at 11:00
You might have had better luck at the wikipage -- which was the top hit when I googled on "brouwer fixed point theorem." (It's odd there was no link to it from the Brouwer bio wikipage.) – Barry Cipra Mar 6 '12 at 18:12
up vote 4 down vote accepted

The general theorem was first given in:

Brouwer, L. E. J. Über Abbildung von Mannigfaltigkeiten. Math. Ann. 71, 97-115. Berichtigung ebd. S. 598 (1912).

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See in particular p. 114, Folgerungen 1,2,3 – Francesco Polizzi Mar 6 '12 at 10:55
Thank you. What is the difference between the three Folgerungen? Sorry but I don't know a word of German and it's also impossible to copy the text and try a google a translation. – Valerio Capraro Mar 6 '12 at 11:05
The usual fixed point theorem is actually in the very last sentence: "Satz 4: Eine eindeutige und stetige Transformation eines n-dimensionalen Elementes in sich besitzt sicher einen Fixpunkt." Translation: "Theorem 4: A continuous transformation of an n-dimensional element in itself has certainly a fixed point." A n-dimensional element is a homeomorphic copy of a n-dimensional simplex. – Michael Greinecker Mar 6 '12 at 11:16
Thank you very much again! – Valerio Capraro Mar 6 '12 at 12:05

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