Suppose \(\mathcal{T}_{1} \subseteq \mathcal{T}_{2}\) are topologies on a set \(X\). Then \(\mathcal{T}_{1}\) is coarser than \(\mathcal{T}_{2}\) and \(\mathcal{T}_{2}\) is finer than \(\mathcal{T}_{1}\). Coarse known as weaker topology. Coarse as in bigger elements. Indiscrete is most coarse.