Let $T_X = (X, \mathcal{P}(X))$ be a D1110: Discrete topological space.

Let $T_Y = (Y, \mathcal{T}_Y)$ be a D1106: Topological space.

Let $f : X \to Y$ be a D18: Map from $X$ to $Y$.

Let $T_Y = (Y, \mathcal{T}_Y)$ be a D1106: Topological space.

Let $f : X \to Y$ be a D18: Map from $X$ to $Y$.

Then $f$ is a D55: Continuous map from $T_X$ to $T_Y$.