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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is separable when there is a [[countable|0ZG61TFBES]] subset $D \\subseteq X$ that is [[dense|0D198GPMTJ]] in $X$.\n\n## Remarks\n\nThe real line is separable, because $\\mathbb{Q}$ is countable and dense. In the same way $\\mathbb{R}^n$ is separable, with the dense set $\\mathbb{Q}^n$.\nEach [[second-countable space|00RE1R4W7N]] is separable. For metric spaces, the converse is also true.\nAn uncountable set with the [[discrete metric|0NA4FK7B8S]] is not separable, because each dense subset is the whole set.\n\n## Explanations\n\n### L1 human\n\nA list of points can approximate a separable space. Each point of the space has points of the list as close as you want.\nFor $\\mathbb{R}$, the list of all fractions does the job.\n",
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