# Definition:Discontinuity

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## Definition

Let $T_1$ and $T_2$ be topological spaces.

Let $f: T_1 \to T_2$ be a mapping from $T_1$ to $T_2$.

Let $D \in T_1$ be an element of $T_1$ such that $f$ is discontinuous at $D$.

Then $D$ is called a **discontinuity (on $f$)**.

### Real Analysis

A **discontinuity** is an element $D$ in the domain of a real function $f$ at which $f$ is discontinuous.

## Also see

- Results about
**discontinuities**can be found**here**.

## Linguistic Note

The word **discontinuity**, as well as meaning an element of the domain at which a mapping is discontinuous, can also be used in the abstract sense as meaning **the property of being discontinuous**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**discontinuity** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**discontinuity**