Remark 3.6.6.3. Suppose we are given a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [r] \ar [d]^{q'} & X \ar [d]^{q} \\ S' \ar [r] & S } \]
in the category of topological spaces. If $q$ is a Serre fibration, then $q'$ is also a Serre fibration.