Definition:Discrete Topology

Definition
Let $A \ne \varnothing$ be a set.

Let $\tau = \mathcal P \left({A}\right)$ be the power set of $A$.

Then $\tau$ is called the discrete topology on $A$ and $\left({A, \tau}\right) = \left({A, \mathcal P \left({A}\right)}\right)$ the discrete space on $A$, or just a discrete space.

Also see

 * Properties of Discrete Topology