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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]].\nFor $x, y \\in X$, write $x \\simeq y$ when there is a [[path|0K0GE6BCYW]] in $X$ from $x$ to $y$.\nThis is an [[equivalence relation|0SGTMBEWRF]] on $X$. Its classes are the path components of $X$.\n\n## Remarks\n\nThe relation is reflexive by constant paths, symmetric by $t \\mapsto \\gamma(1 - t)$, and transitive by joining two paths one after the other.\nThe path component of $x$ is the largest path-connected subset of $X$ that contains $x$.\nEach path component lies in a [[connected component|0NRT0E2QT2]]. The [[topologist's sine curve|0K3T4A659R]] is one connected component but has two path components.\nPath components need not be closed.\n\n## Explanations\n\n### L1 human\n\nThe path component of a point is the set of all points that you can reach from it along a path.\n",
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