\begin{definition}[Definition:Open Mapping]
Let $\struct {S_1, \tau_1}$ and $\struct {S_2, \tau_2}$ be topological spaces.
Let $f: S_1 \to S_2$ be a mapping. 
Then $f$ is said to be an '''open mapping''' {{iff}}:
:$\forall U \in \tau_1: f \sqbrk U \in \tau_2$
where $f \sqbrk U$ denotes the image of $U$ under $f$.
\end{definition}