Definition:Discrete Topology

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

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

Then $$\vartheta$$ is called the discrete topology on $$A$$ and $$\left\{{A, \vartheta}\right\}$$ a discrete space.

It is clear from the definition of topology that $$\vartheta$$ is indeed a topology on $$A$$.