# surjective open maps in terms of nets

Theorem - Let $f:X\u27f6Y$ 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 ${y}_{i}\u27f6y$, then for every $x\in {f}^{-1}(\{y\})$ there exists a subnet ${\{{y}_{{i}_{j}}\}}_{j\in J}$ that