Example 2

Let $X$ be the sum of a family $(X_i)$ of subspaces of $X$, and let $X/R$ be the space obtained by pasting together the $X_i$ along open subsets $A_{ix}$ by means of bijections $h_{ix}$ (§ 2, no. 5); and suppose that $h_{ix}$ is a homeomorphism of $A_{ix}$ onto $A_{x'}$ for each pair of indices $(i, x)$.

Then the relation R is open. For if U is open in X, the saturation of U is the union of the $h_{x!}(U \cap A_{ix})$; since $U \cap A_{ix}$ is open in $A_{ix}$, $h_{x!}(U \cap A_{ix})$ is open in $A_{ix}$ and therefore in X.