Definition:Continuous Real-Valued Function Space

Definition

Let $X$ be a topological space.

Let $f : X \to \R$ be a continuous real valued mapping.

Then the set of all such mappings $f$ is known as continuous real-valued function space and is denoted by $\map C X$:

$\map C X := \map C {X, \R} = \set {f : X \to \R}$

Sources

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