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 $T = \left({X, \vartheta}\right)$ are $\varnothing$ and $X$.

Also see

 * Indiscrete topology, also known as a trivial topology.

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