# surjective open maps in terms of nets

Theorem - Let $f:X\longrightarrow Y$ be a surjective map between the topological spaces $X$ and $Y$. Then $f$ is an open mapping if and only if given a net $\{y_{i}\}_{i\in I}\subset Y$ such that $y_{i}\longrightarrow y$, then for every $x\in f^{-1}(\{y\})$ there exists a subnet $\{y_{i_{j}}\}_{j\in J}$ that