Let \(X\) be a topological space. For \(x, y\in X\) write \(x\sim y\) if there is a connected subspace \(C\subseteq X\) with \(x, y\in C\). The equivalence classes of \(\sim\) are the connected components of \(X\).
The relation \(\sim\) is an equivalence relation on \(X\).
See [@Mun00].