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  "body": "\n## Summary\n\nA Lindelöf space is a [[topological space|0CQHFPGJ45]] in which every [[open cover|049PXYHW1T]] has a countable subcover.\nIt is a weakening of [[compactness|0TVJZYB6SH]], where finite subcovers are replaced by countable ones.\nEvery [[second-countable space|03PPNCM9GG]] is Lindelöf, and every regular Lindelöf space is [[paracompact|8R29G6NG9Q]].\nFor [[metric spaces|0VKD1TP7F3]], being Lindelöf, [[separable|0Z2P41SVDP]] and second-countable are the same.\n\n## Explanations\n\n### L1 human\n\nCompactness says that finitely many members of any open cover always suffice to cover the space.\nThe Lindelöf property says that countably many always suffice.\nThe real line is not compact, since the intervals $(-n, n)$ cover it and no finitely many of them do.\nIt is Lindelöf, since it has a countable base of open intervals with rational end points.\nAn uncountable set with the discrete topology is not Lindelöf, because the cover by single points has no countable subcover.\n",
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