Definition:Continuous Real Function/Class

Definition

The class of continuous real functions is often denoted $C$.

Hence:

$\map f x \in C$ at $a$

if and only if:

$\ds \lim_{x \mathop \to a} \map f x = \map f a$

Sources

• 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 2$. Functions of One Variable: $2.1$ Limits and Continuity