\begin{definition}[Definition:Continuous Mapping Space]
Let $X, Y$ be topological spaces.
Let $f : X \to Y$ be a continuous mapping.
Then the set of all such mappings $f$ is known as '''continuous mapping space''' and is denoted by $\CC \paren {X,Y}$:
:$\CC \paren {X, Y} = \set {f : X \to Y}$
\end{definition}