Homotopy excision theorem
= Homotopy excision theorem
{title2=$\pi_i(B,A)\longrightarrow\pi_i(B\cup_A C,C)$}
For a based CW triad with connected intersection $A$, if $(B,A)$ is $p$-connected and $(C,A)$ is $q$-connected, $p,q\ge1$, the comparison map is an <isomorphism> for $i<p+q$ and a surjection for $i=p+q$. This connectivity form of the Blakers-Massey theorem controls the failure of ordinary relative <homotopy> to satisfy unrestricted excision.