Example 1

Take for space X the ball $\mathbf{B}_n$ and for subspace A the sphere $\mathbf{S}_{n-1}$. If V = X$-\{0\}$, there exists a strong contraction of V onto $\mathbf{S}_{n-1}($III, p. 237, example). Hence the pair $(\mathbf{B}_n,\mathbf{S}_{n-1})$ possesses the homotopy extension property.