# lifting of maps

Let $p\colon\thinspace E\to B$ and $f\colon\thinspace X\to B$ be (continuous) maps. Then a lifting of $f$ to $E$ is a (continuous) map $\tilde{f}\colon\thinspace X\to E$ such that $p\circ\tilde{f}=f$. The terminology is justified by the following commutative diagram