Examples of zero-dimensional spaces are: the set $\mathbb{Q}$ of rational numbers (with subspace topology induced from the usual metric topology on $\mathbb{R}$, the set of real numbers), the Cantor space, as well as the Sorgenfrey line.

The concepts of zero-dimentionality and total disconnectedness are closely related. Indeed, every zero-dimentional $T_{1}$ space is totally disconnected. Furthermore, if a topological space is locally compact and Hausdorff, then the notions of zero-dimentionality and total disconnectedness are equivalent.