lifting of maps

Let $p\\colon\\thinspace E\\to B$ and $f\\colon\\thinspace X\\to B$ be (continuous) maps. Then alifting 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

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