Example 2

*Here are other cases in which the pair $(X,A)$ possesses the homotopy extension property.

(i) The space X is a paracompact differentiable manifold of class $C^1$ and A a closed submanifold of X. In view of corollary1, this follows from the fact that X is perfectly normal (IX, p. 103, exerc. 11) and that A possesses a tubular neighbourhood in X;

(ii) The space X is a cellular space and A a full subspace with respect to a given cellular decomposition of X.*