Definition:Continuous Mapping Space

Definition

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 $C \paren {X,Y}$:

$C \paren {X, Y} = \set {f : X \to Y}$

See also

• Definition:Continuous Mapping

Sources

• 2013 : Philippe G. Ciarlet: Linear and Nonlinear Functional Analysis with Applications: Main Notations