Definition:Indiscrete Topology

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

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

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

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

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

Also known as

 * The trivial topology (on $S$)
 * The nondiscrete topology (on $S$)

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.