The Poincaré-Miranda theorem. (English) Zbl 0891.47040

Kulpa, Wladyslaw

Am. Math. Mon. 104, No. 6, 545-550 (1997).

The author makes some interesting remarks on Brouwer’s fixed point theorem, Sperner’s combinatorial lemma, and Poincaré’s “higher-dimensional” intermediate value theorem in their historical contexts.

Reviewer: J.Appell (Würzburg)

MSC:

47H10	Fixed-point theorems
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

Poincaré’s higher-dimensional intermediate value theorem; Brouwer’s fixed point theorem; Sperner’s combinatorial lemma