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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is totally disconnected when each [[connected subset|0R37DFJKFW]] of $X$ has at most one point.\n\n## Remarks\n\nEquivalently, each connected component of $X$ is a single point.\nEach [[discrete space|0S2TEHX4E1]] is totally disconnected. So are $\\mathbb{Q}$ and $\\mathbb{R} \\setminus \\mathbb{Q}$, as subspaces of $\\mathbb{R}$.\nThe [[Cantor set|0BXNDZFQME]] is totally disconnected, although it is compact and has no isolated points.\n\n## Explanations\n\n### L1 human\n\nA totally disconnected space falls apart into single points: no subset with two or more points is in one piece.\nThis does not mean that the space is discrete. The rationals are a good example.\n",
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