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 $f$).