mapping space in Top

Let \((X,\mathcal{T})\) and \((Y,\mathcal{T}_Y)\) be topological spaces and

\begin{align*} \mathcal{C}(X,Y) = \mathrm{Hom}_{\mathrm{Top}}(X,Y) \end{align*}

the hom-set, i.e. the set of continuous maps

A mapping space is a topology on \(\mathcal{C}(X,Y)\) with nice properties see:

• compact open topology