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  "body": "\n## Summary\n\nA compactification of a [[topological space|0CQHFPGJ45]] $X$ is a [[compact space|0TVJZYB6SH]] that contains a copy of $X$ as a [[dense|0BSJSX7ME2]] subspace.\nIt adds \"points at infinity\" so that sequences or nets that escape $X$ get limits.\nStandard examples are the [[one-point compactification|0GWN3CMRK8]] and the [[Stone–Čech compactification|D9MWP5C85W]].\nA space has a Hausdorff compactification exactly when it is a [[Tychonoff space|C5N2J2K6Z3]].\n\n## Explanations\n\n### L1 human\n\nThe open interval $(0, 1)$ is not compact, because points can run toward the missing ends.\nAdding the two end points gives $[0, 1]$, a compactification of $(0, 1)$.\nBending the real line into a circle and adding one point at the top gives another compactification, of $\\R$.\nDifferent compactifications of the same space add different sets of ideal points.\n",
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