Exercise 3, § 5

Soit $((X_i, x_i))_{i\in I}$ a family of pointed topological spaces; let $(X, x)$ denote the bouquet of this family (IV, p. 421, example 4). Suppose that, for every $i\in I$, the point $x_i$ is closed in $X_i$ and possesses a fundamental system of neighbourhoods V such that the group $\pi_1(V, x_i)$ is reduced to the identity element. Then the canonical homomorphism $_i*_{\in I}\pi_1(X_i, x_i)\rightarrow \pi_1(X, x)$ is an isomorphism.