ISSN : 1226-0657
A holomorphic function f on D = {z : │z│ < 1} is called uniformly locally univalent if there exists a positive constant <TEX>$\rho$</TEX> such that f is univalent in every hyperbolic disk of hyperbolic radius <TEX>$\rho$</TEX>. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.