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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is connected when there are no [[open sets|01ZQQDCERP]] $U, V \\subseteq X$ with $U \\neq \\varnothing$, $V \\neq \\varnothing$, $U \\cap V = \\varnothing$ and $U \\cup V = X$.\n\n## Remarks\n\nEquivalently, the only subsets of $X$ that are both open and [[closed|0G5AV9Q4RR]] are $\\varnothing$ and $X$.\nEquivalently, each [[continuous map|0SY9ECQ19Q]] from $X$ to the discrete space $\\{0, 1\\}$ is constant.\nThe interval $[0, 1]$ is connected. The set $[0, 1] \\cup [2, 3]$ is not connected.\nUnder this definition the empty space is connected. Some authors require a connected space to be nonempty.\n\n## Explanations\n\n### L1 human\n\nA connected space cannot be split into two separate open parts.\nConnectedness is the topological form of the idea that a space is in one piece.\n",
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