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

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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 $C \closedint a b$:

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