Suppose $f:E\rightarrow B$ has the right lifting property with respect to all CW-pairs $(X,A)$. Then $f$ is a Serre fibration and also a weak-homotopy equivalence. But want i want to prove is the following: Suppose $B$ is a CW-complex. Then $f$ admits a section.
My idea was to take the CW-pair $(B,\varnothing)$, but the question is, is this the good choice or has one to use other deep theorems about that?
Thanks a lot.