One example would be a map induced by a morphism f: X \to Y in the long homology sequence.

E.g. suppose the top row is a cohomology of pair (X, A) and the bottom row is the cohomology of pair (Y, B). Then the theorem says that the H^n(X, A) can be squeezed between the n-th and n-1-th cohomology of X and A, because any morphism inducing isomorphism on those extends to H^n(X, A).

One example would be a map induced by a morphism $f: X \to Y$ in the long homology sequence.

E.g. suppose the top row is a cohomology of pair $(X, A)$ and the bottom row is the cohomology of pair $(Y, B)$. Then the theorem says that the $H^n(X, A)$ can be squeezed between the $n$-th and $(n-1)$-th cohomology of $X$ and $A$, because any morphism inducing isomorphism on those extends to $H^n(X, A)$.

One example would be a map induced by a morphism f: X \to Y in the long homology sequence.

One example would be a map induced by a morphism f: X \to Y in the long homology sequence.

E.g. suppose the top row is a cohomology of pair (X, A) and the bottom row is the cohomology of pair (Y, B). Then the theorem says that the H^n(X, A) can be squeezed between the n-th and n-1-th cohomology of X and A, because any morphism inducing isomorphism on those extends to H^n(X, A).