Definition:Trivial Topological Space

Definition
A trivial topological space is a topological space with only one element.

The open sets of a trivial topological space $T = \left({\left\{{s}\right\}, \tau}\right)$ are $\varnothing$ and $\left\{{s}\right\}$.

Also see

 * Indiscrete topology, also known as a trivial topology.

This is not the same as a trivial topological space unless its underlying set is a singleton.