. (10 points) Let (X, dx) and (Y, dy) be two metric spaces and let f : X → Y be a bijective function. Show that the following are equivalent:

\text { 1) both } f \text { and its inverse } f^{-1} \text { are continuous; } \text { 2) } f(\bar{A})=\overline{f(A)} \text { for every subset } A \text { of } X \text {. }