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  "body": "\n## Summary\n\nAn entourage of a [[uniform space|A54T86KS63]] is one of the sets of pairs of points that make up its uniform structure.\nEach entourage stands for one degree of closeness: the pairs in it are the pairs of points that are close to that degree.\nEntourages replace the numbers $\\varepsilon$ of metric spaces in the definitions of uniform continuity, Cauchy filters and completeness.\n\n## Explanations\n\n### L1 human\n\nIn a metric space, the pairs $(x, y)$ with distance less than $\\varepsilon$ form a set of pairs, a relation on the space.\nSuch sets, and all larger ones, are the entourages of the metric.\nFor $\\R$ and $\\varepsilon = 1$, the entourage is the open band $\\set{(x, y) : \\abs{x - y} \u003c 1}$ around the diagonal of the plane.\nSmaller entourages are thinner bands, and so they say \"closer\".\n",
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