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  "body": "\n## Summary\n\nA family of subsets of a [[topological space|0CQHFPGJ45]] is locally finite if each point has a [[neighbourhood|0ZCY0Z80B6]] meeting only finitely many members.\nThe family may be infinite, but near each point it looks finite.\nLocal finiteness lets one treat infinite unions and sums as if they were finite.\nFor example, the closure of the union of a locally finite family is the union of the closures.\nIt is the key notion in the definition of [[paracompact spaces|8R29G6NG9Q]] and of partitions of unity.\n\n## Explanations\n\n### L1 human\n\nThink of tiles on an infinite floor: there are infinitely many tiles, but around any spot you stand on, only a few tiles are close by.\nThe intervals $[n, n + 1]$ for integers $n$ form such a family on the real line.\nThe intervals $(0, 1/n)$ for $n \\ge 1$ do not, because every small interval around $0$ meets all of them.\n",
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