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.