Definition:Discrete Topology

Definition
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.

Linguistic Note
Be careful how you spell this. A common homophone horror is to refer to this as the discreet topology.

However, discreet means cautious or tactful, and describes somebody who is able to keep silent for political or delicate social reasons.