Definition:Discontinuity

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