Continuous lift
= Continuous lift
{title2=$p\widetilde f=f$}
For <continuous maps> $p:E\to B$ and $f:X\to B$, a <continuous lift> of $f$ through $p$ is a <continuous map> $\widetilde f:X\to E$ with $p\widetilde f=f$. Existence and uniqueness require additional hypotheses; the <lifting criterion for a covering space> states a useful existence criterion when $p$ is a <covering map> and $X$ is <path-connected> and <locally path-connected>.