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  "body": "\n## Summary\n\nA perfect map is a [[continuous|0VGFHTM75Y]] [[closed map|00FSJTXPJM]] onto its target whose fibres are all [[compact|0TVJZYB6SH]].\nPerfect maps carry many properties, such as compactness, local compactness and paracompactness, in both directions between the source and the target.\nThey are a central tool of general topology for comparing spaces.\n\n## Explanations\n\n### L1 human\n\nUnder a perfect map, each point of the target comes from a compact piece of the source, and the space is not torn.\nClosedness means that the image of a closed set has no missing limit points.\nThe projection of the cylinder $S^1 \\times \\R$ onto the line $\\R$ is perfect: each fibre is a circle, which is compact.\nThe projection of the plane onto a line is not, since each fibre is a whole line.\n",
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