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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CQHFPGJ45]].\nThe space $X$ is *zero-dimensional* if it has a base consisting of [[clopen sets|DQ4E55T3BW]], that is, of sets that are both open and closed.\n\n## Remarks\n\nExample: $\\Q$ with the subspace topology from $\\R$ is zero-dimensional.\nFor irrational numbers $a \u003c b$, the set $\\Q \\cap (a, b) = \\Q \\cap [a, b]$ is clopen in $\\Q$.\nThese sets form a base, since irrational numbers are dense in $\\R$.\n\nNon-example: $\\R$ is not zero-dimensional.\nSince $\\R$ is [[connected|0V032VWTHD]], its only clopen sets are $\\emptyset$ and $\\R$, and they do not form a base.\n\nSome authors define zero-dimensional by [[Lebesgue covering dimension|A3W7RGXXK9]] zero instead.\nThe two definitions agree for separable metric spaces, but not for all spaces.\n",
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