Let \(X\) be a set and \(\mathcal{T}=\{\emptyset, X\}\). Then \((X,\mathcal{T})\) is a topological space and \(\mathcal{T}\) is called trivial topology on \(X\).
Example
The topology of the quotient space
\(\mathbb{R}/\mathbb{Q}\) is the trivial topology.