Exercise 14, § 3

Let $X$ be a topological space which is the sum of two subspaces $X_1$ and $X_2$, and let $X/R$ be the space obtained by pasting together $X_1$ and $X_2$ along a subspace $A_1$ of $X_1$ and a subspace $A_2$ of $X_2$ by means of a homeomorphism $h$ of $A_1$ onto $A_2$. Show that the canonical images of $X_1$ and $X_2$ in $X/R$ are homeomorphic to $X_1$ and $X_2$ respectively.