Let $(X,\tau)$ be a [topological space](/page/Topological%20Space). Define a relation $\sim_p$ on $X$ by declaring that, for $x,y \in X$, one has $x \sim_p y$ if and only if there exists a path in $X$ from $x$ to $y$. Then $\sim_p$ is an [equivalence relation](/page/Equivalence%20Relation) on $X$.