Definition:Indiscrete Topology

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

Let $\vartheta = \left\{{A, \varnothing}\right\}$.

Then $\vartheta$ is called the indiscrete topology on $A$.

It is also called the trivial topology on $A$.

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

A topological space $\left({A, \left\{{A, \varnothing}\right\}}\right)$ is known as an indiscrete space.

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

However, indiscreet means incautious or tactless. It's how you describe somebody who cannot keep a secret.