Let $T_X = (X, \mathcal{T}_X)$ and $T_Y = (Y, \mathcal{T}_Y)$ each be a D1106: Topological space.
The set of continuous maps from $T_X$ to $T_Y$ is the D11: Set $$\begin{equation} C(T_X \to T_Y) : = \{ f \mid f : X \to Y \text{ is continuous from } T_X \text{ to } T_Y \} \end{equation}$$