Example 4

Let E be a principal fibre space with base B and group G and let F be a topological space. The $(B\times F)$-space $E\times F$ endowed with the law of operation $(x, y)\cdot g= (x\cdot g, y)$, for $x\in E,y\in F$ and $g\in G$, is a principal fibre space with group G. This is the particular case of Example 2, where $p'$ is the identity mapping of F and $G'$ is a group reduced to the identity element.