Let $T_X = (X, \mathcal{T}_X)$ and $T_Y = (Y, \mathcal{T}_Y)$ each form a D1106: Topological space.
A D18: Map $f : X \to Y$ is open from $T_X$ to $T_Y$ if and only if \begin{equation} \forall \, U \in \mathcal{T}_X : f(U) \in \mathcal{T}_Y \end{equation}