Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101A COVERING PROPERTY IN PRINCIPAL BUNDLES9198109310.22044/jas.2018.1093ENA. PakdamanDepartment of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.M. AttaryDepartment of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.Journal Article20150802Let $p:X\lo B$ be a locally trivial principal G-bundle and $\wt{p}:\wt{X}\lo B$ be a locally trivial principal $\wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $\wt{G}$ is a covering group of $G$ if and only if $\wt{X}$ 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 $\pi(X,x_0)$-bundle, for every $x_0\in X$.https://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf