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  "body": "\n## Example\n\nLet $X$ be a set and let $\\tau$ consist of $\\varnothing$ and of all sets $U \\subseteq X$ whose complement $X \\setminus U$ is [[finite|0BBTH3YSZA]].\nThen $\\tau$ is a [[topology|0CNQXVBHCX]] on $X$, the cofinite topology.\n\n## Remarks\n\nThe closed sets are $X$ and the finite subsets of $X$.\nThe cofinite topology is [[T1|05GQJXBP3F]]: each one-point set is closed.\nIf $X$ is infinite, any two nonempty open sets meet. Thus the space is not [[Hausdorff|0MXB4CKHFW]].\nEach space with the cofinite topology is [[compact|0QPHW703PV]].\n\n## Explanations\n\n### L1 human\n\nIn the cofinite topology, a set is open when it misses only finitely many points.\nOn an infinite set, open sets are very large, so no two nonempty open sets are disjoint.\n",
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