# Category:Definitions/Piecewise Continuous Functions

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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 $\openint {x_{i − 1} } {x_i}$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Piecewise Continuous Functions"

The following 14 pages are in this category, out of 14 total.

### P

- Definition:Piecewise Continuous Function
- Definition:Piecewise Continuous Function with Improper Integrals
- Definition:Piecewise Continuous Function with One-Sided Limits
- Definition:Piecewise Continuous Function/Also known as
- Definition:Piecewise Continuous Function/Bounded
- Definition:Piecewise Continuous Function/Improper Integrals
- Definition:Piecewise Continuous Function/One-Sided Limits
- Definition:Piecewise Continuous Function/Variant 1
- Definition:Piecewise Continuous Function/Variant 2
- Definition:Piecewise Continuous Function/Variant 3
- Definition:Piecewise Continuously Differentiable Function
- Definition:Piecewise-Continuous Function