The Brouwer's plane translation theorem asserts that for a fixed point free orientation preserving homeomorphism f of the plane, every point belongs to a proper topological imbedding C of R, disjoint from its image and separating and . Such a curve is called a Brouwer line. We prove that we can construct a foliation of the plane by Brouwer lines.
Cite this article
Patrice Le Calvez, Une version feuilletée du théorème de translation de Brouwer. Comment. Math. Helv. 79 (2004), no. 2, pp. 229–259