Definition:Indiscrete Topology

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.