# Image of a patch - an open set?

"Prove that if $y:E\rightarrow M$ is a proper patch, then y carries open sets to open sets in M. Deduce that if $x D\rightarrow M$ is an arbitrary patch, then the image x(D) is an open set in M. (Hint: To prove the latter assertion, use corollary 3.3)"
Corollary 3.3 is "If x and y are patches in a surface M whose images overlap, then the composite functions $x^{-1}y$ and $y^{-1}x$ are differentiable mappings defined on open sets of $E^2$.