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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $(X, \\tau)$ is second-countable when $\\tau$ has a [[basis|06EX0FHBTF]] $\\mathcal{B}$ that is [[countable|0ZG61TFBES]].\n\n## Remarks\n\nThe space $\\mathbb{R}^n$ is second-countable: the open balls with rational centres and rational radii form a countable basis.\nEach second-countable space is [[separable|0GKJ78948V]] and [[first-countable|0HG11FW8MJ]].\nA metric space is second-countable if and only if it is separable.\nAn uncountable set with the [[discrete topology|0S2TEHX4E1]] is not second-countable.\n\n## Explanations\n\n### L1 human\n\nA second-countable space has a countable list of open sets from which you can build every open set by unions.\nFor $\\mathbb{R}$, the open intervals with rational endpoints form such a list.\n",
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