a covering property in principal bundles

. let p : x → b be a locally trivial principal gp : x → b be a locally trivial principal g-bundle. in this paper, by using the structure of principal bundles according to transition functions, we show that g is a covering group of g if and only if x is a covering space of x. then, we conclude that a topological space x with non-simply connected universal covering space has no connected locally trivial principal π(x, x0)-bundle, for every x0 ∈ x.