2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61995We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$ intersects W then there is a fixed point in W. Consequently, if the omega limit set of every point is nonempty and uniformly bounded then there is a fixed point.4 pages, minor clarificationsDynamical Systems54H25 (Primary), 37B30, 37B25 (Secondary)text