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Let T be an orientation-preserving homeomorphism of the plane E onto itself. Suppose that T has no fixed points, i.e., that on the sphere 5 2 = EW{ <*> }, T has no fixed point other than oo. Then, by the Brouwer Translation Theorem [ l ] , one can construct a Jordan curve TC.S in such a manner that r P \ 7 T = { °° }. If p is a preassigned point in E, then T can be made so that p lies between T and I T . In the present note we state two new results (Lemma 1 and Theorem 1) about the homeomorphisms treated in Brouwer's theorem. The proofs, which depend to some extent upon Brouwer's techniques, will appear elsewhere. Having presented these results, we will apply them to the problem of embedding homeomorphisms in flows. Indeed, we obtain a natural characterization of those homeomorphisms of the plane which are equivalent to translations.

On homeomorphisms of the plane, and their embedding in flows