A COVERING PROPERTY IN PRINCIPAL BUNDLES

Document Type : Original Manuscript

Authors

Department of Mathematics, University of Golestan, P.O.Box 155, Gorgan, Iran.

Abstract

Let

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

π (X, x_{0})

-bundle, for every

x_{0} \in X

Keywords