Definition:Continuous Mapping Space
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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
Sources
- 2013 : Philippe G. Ciarlet: Linear and Nonlinear Functional Analysis with Applications: Main Notations