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 $p:Xlo B$ 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 $x_0in X$.http://jas.shahroodut.ac.ir/article_1093_2fa7e7be0e8cdd89821d84d3247cd729.pdf