Category:Definitions/Piecewise Continuous Functions

This category contains definitions related to Piecewise Continuous Functions.
Related results can be found in Category:Piecewise Continuous Functions.

Let $f$ be a real function defined on a closed interval $\closedint a b$.

$f$ is piecewise continuous if and only if:

there exists a finite subdivision $\set {x_0, x_1, \ldots, x_n}$ of $\closedint a b$, where $x_0 = a$ and $x_n = b$, such that:

for all $i \in \set {1, 2, \ldots, n}$, $f$ is continuous on $\openint {x_{i − 1} } {x_i}$.