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  "body": "\n## Summary\n\nA net in a space $X$ is a family of points of $X$ indexed by a directed set.\nIt generalizes a sequence, which is indexed by $\\N$.\nConvergence of nets is defined just as for sequences: eventually the net stays in every neighbourhood of the limit.\nIn every [[topological space|0CQHFPGJ45]], nets describe closures, continuity, compactness and the Hausdorff property, which sequences do only in special spaces.\nNets are an alternative to the [[convergence of filters|70M1VAPFN0]], and the two languages are equivalent.\n\n## Explanations\n\n### L1 human\n\nA sequence moves forward along $1, 2, 3, \\dots$.\nA net moves forward along any set of indices where any two indices have a common later index.\nFor example, the finite subsets of a set, ordered by inclusion, form such an index set; this is how infinite sums over arbitrary sets are defined.\nA net converges to a point when, from some index on, all its points stay as close to the point as one wants.\n",
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