Summary: Let \((X,b)\) be a partial \(b\)-metric space with coefficient \(s \geq 1\). For each \(x \in X\) and each \(\varepsilon>0\), put \(B(x,\varepsilon)=\{y\in X:b(x,y)<b(x,x)+\varepsilon\}\) and put \(\mathcal B=\{B(x,\varepsilon): x\in X\text{ and }\varepsilon>0\}\). In this brief note, we prove that \(\mathcal B\) is not a base for any topology on \(X\), which shows that a claim on partial \(b\)-metric spaces is not true. However, \(\mathcal B\) can be a subbase for some topology \(\tau\) on \(X\). For a sequence in \(X\), we also give some relations between convergence with respect to \(\tau\) and convergence with respect to \(b\).