Definition: A function $f$ is said to be an open mapping if the image of every open set in its domain is itself open. So: If we have $f:K \rightarrow \mathbb{C}$, where $K \subseteq D$ , $D$ is the domain of analyticity of $f$.
Then $f$ maps $K^\circ$ to $(f(K))^\circ$ and $\partial(K)$ to $\partial f(K)$, where $\partial K $ denote the boundary of $K$?