= Splitting of a simply connected Eilenberg–MacLane fibration
{title2=$H^{n+1}(B;G)=0\Rightarrow E\simeq_{\mathrm w}B\times K(G,n)$}
For a <Serre fibration> with this fiber over a simply connected CW base, the fiber identity class has only one possible nonzero outgoing differential in the <cohomological Serre spectral sequence>, landing in $H^{n+1}(B;G)$. If that group vanishes, the class extends to the CW total space. Its representing map, paired with projection to $B$, is an isomorphism on fiber and base <homotopy groups> and hence a <weak homotopy equivalence> to the product.
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