Proposition 9

Suppose that the $h_{\mu \lambda}$ are homeomorphisms and that each $A_{\lambda \mu}$ is open (resp. closed) in $X_\lambda$; then each $\varphi(X_\lambda)$ is open (resp. closed) in $X/R$ and the restriction of $\varphi$ to $X_\lambda$ is a homeomorphism of $X_\lambda$ onto the subspace $\varphi(X_\lambda)$ of $X/R$.