covariant compact open functor

given category Top and a topological space \((X, \mathcal{T})\) the contravariant compact open functor is defined

\begin{align*} \mathrm{Map}_X: \mathrm{Top} \rightarrow& \mathrm{Top} \\ (Y) \mapsto& \mathcal{C}(X,Y) \\ (f: Y \rightarrow Z) \mapsto& (f^{ \leftarrow}: \mathcal{C}(X,Y) \rightarrow \mathcal{C}(X,Z)) \end{align*}

follows from compact open bifunctor