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  "body": "\n## Summary\n\nA clopen set in a [[topological space|0CQHFPGJ45]] is a subset that is both [[open|02BH3MCBQB]] and [[closed|0ZCK8DQYN1]].\nThe empty set and the whole space are always clopen.\nA space is [[connected|0V032VWTHD]] exactly when it has no other clopen sets, so clopen sets measure how a space splits into pieces.\n\n## Explanations\n\n### L1 human\n\nUsually \"open\" and \"closed\" look like opposite properties, but a set can have both.\nPicture a space made of two separate islands: each island is open, and its complement, the other island, is open too, so each island is also closed.\nFor example, in the space $[0, 1] \\cup [2, 3]$ with the usual distance, the piece $[0, 1]$ is clopen.\nIn the real line $\\R$ itself, only $\\emptyset$ and $\\R$ are clopen, because $\\R$ is in one piece.\n",
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