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  "body": "\n## Summary\n\nAn extremally disconnected space is a [[topological space|0CQHFPGJ45]] in which the [[closure|0QEAJB91GZ]] of every open set is open.\nEquivalently, any two disjoint open sets have disjoint closures.\nCompact Hausdorff extremally disconnected spaces are exactly the Stone spaces of complete [[Boolean algebras|0XADJKM699]].\nBy [[Gleason's theorem|CPZKZ2AV0G]], they are also the projective objects among compact Hausdorff spaces.\n\n## Explanations\n\n### L1 human\n\nIn most familiar spaces, the closure of an open set adds a boundary that is not open.\nFor example, the closure of $(0, 1)$ in $\\R$ is $[0, 1]$, and $[0, 1]$ is not open.\nIn an extremally disconnected space this never happens: closures of open sets stay open.\nDiscrete spaces and the Stone–Čech compactification $\\beta \\N$ are examples.\n",
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