# Definition:Continuous Real Function/Closed Interval/Definition 2

Let $f$ be a real function defined on a closed interval $\left[{a \,.\,.\, b}\right]$.
The function $f$ is continuous on $\left[{a \,.\,.\, b}\right]$ if and only if it is continuous at every point of $\left[{a \,.\,.\, b}\right]$.