Funciones localmente inyectivas entre continuos

a map f between topological spaces is called locally one to one provided that for every point x there exists an open set u such that x∈ u and f|u is one to one. we study properties of this kind of maps, when they are defined from a continuum onto itself. also, we show necesary and sufficient conditions that a continuum x must satisfy to prove the following: if \hboxf:x→ x is locally one to one, then f is a homeomorphism.