Une version feuilletée du théorème de translation de Brouwer

Abstract

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 $f(C)$ and $f^{-1}(C)$. Such a curve is called a Brouwer line. We prove that we can construct a foliation of the plane by Brouwer lines.