Definition:Space of Real-Valued Functions Continuous on Closed Interval

Definition

Let $f : \closedint a b \to \R$ be a continuous real valued function.

Then the set of all such mappings $f$ is known as continuous on closed interval real-valued function space and is denoted by $C \closedint a b$:

$C \closedint a b := C \paren {\closedint a b, \R} = \set {f : \closedint a b \to \R}$

Sources

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