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  "body": "\n## Summary\n\nA uniform space is a set with a uniform structure, a family of [[entourages|FVFFKNKEDF]] that say when two points are close to a given degree.\nIt is the natural setting for [[uniform continuity|0M4JJT780X]], Cauchy filters and completeness, without a metric.\nMetric spaces and topological groups carry uniform structures, and every uniform space has an underlying topology.\n\n## Explanations\n\n### L1 human\n\nIn a metric space one can say that $x$ and $y$ are as close as $u$ and $v$: both distances are below $\\varepsilon$.\nA topology alone cannot compare closeness at different places, but a uniform structure can.\nIt lists the relations \"being $\\varepsilon$-close\" as sets of pairs of points, without numbers.\nFor example, on $\\R$ the sets $\\set{(x, y) : \\abs{x - y} \u003c \\varepsilon}$ for $\\varepsilon \u003e 0$ generate the usual uniform structure.\n",
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