Let $(X,\tau)$ be a [topological space](/page/Topological%20Space), and let $A \subset X$ be equipped with the [subspace topology](/page/Subspace%20Topology) induced by $\tau$. Then $A$ is disconnected if and only if there exists a subset $B \subset A$ such that $B$ is clopen in $A$, $B \neq \varnothing$, and $B \subsetneq A$.