In topology, a **totally disconnected space** is a type of topological space where the only connected subsets are the singletons (sets containing exactly one point) and the empty set. In other words, a topological space \( X \) is totally disconnected if the only connected components of \( X \) are the individual points.
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A topological space is totally disconnected when every nonempty connected subset is a singleton. The empty set is connected under the usual convention and is excluded from this phrasing.