On the struture of homeomorphims of the open annulus
Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a translation and we study the action of $h$ on the compactly connected components of the closed and without interior set ${\bf R}^2 \setminus O$.
Foundations of Point Set Theory
Consequences of axioms 0 and 1 Consequences of axioms 0, 1 and 2 Consequences of axioms 0, 1, 2, 3 and 5 Consequences of axioms 0 and 1-5 Upper semi-continuous collections Consequences of axioms $0, 1, 2, 3, 4, 5_1, 5_2, 6$ and $7$ Concerning topological equivalence and the introduction of distance Appendix Bibliography Glossary.
Une version feuillete quivariante du thorme de translation de Brouwer
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 Brouwer line: a proper topological embedding C of R, disjoint from its image and separating f(C) and f–1(C). Suppose that f commutes with the elements of a discrete group G of orientation preserving homeomorphisms acting freely and properly on the plane. We will construct a G-invariant topological foliation of the plane by Brouwer lines. We apply this result to give simple proofs of previous results about area-preserving homeomorphisms of surfaces and to prove the following theorem: any Hamiltonian homeomorphism of a closed surface of genus g ≥ 1 has infinitely many contractible periodic points.