Corollary

Let G be a connected topological group and locally connected by arcs. Let $G'$ be a connected covering of G, let $p$ be its projection and let $e'$ be an element of the fibre N of the identity element $e$ of G. Endow $G'$ with the unique continuous composition law $m': G'\times G'\rightarrow G'$ such that $p\circ m'=m\circ (p, p)$ and $m'(e', e') =e'$. If $i: N\rightarrow G'$ denotes the canonical injection, $(G', p, i)$ is a central extension of G by N (A, I, p. 63).