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  "body": "\n## Summary\n\nThe order topology is the natural topology on a [[totally ordered set|0FRXBVVR03]], generated by the open rays $\\set{x : x \u003e a}$ and $\\set{x : x \u003c b}$.\nThe usual topology of the real line is the order topology of its usual order.\nOrdinals, the long line and many classical counterexamples of general topology are built as order topologies.\nEvery order topology is Hausdorff, and in fact normal.\n\n## Explanations\n\n### L1 human\n\nOn a line of ordered points, call a set open when, around each of its points, it contains a whole open interval.\nThis is exactly how the open sets of the real line are described, but it uses only the order and not the distance.\nSo any totally ordered set, such as the rationals, the integers or a set of ordinals, gets a topology in the same way.\nOn the integers every point $n$ is the open interval $(n - 1, n + 1)$, so the order topology is discrete.\n",
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