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  "body": "\n## Summary\n\nA morphism of schemes is universally closed if it stays a closed map of topological spaces after every base change.\nBeing closed alone is too weak a condition, because the product topology is not the Zariski topology of a fibre product.\nUniversal closedness is the topological half of the definition of a proper morphism.\n\n## Explanations\n\n### L1 human\n\nA closed map sends closed sets to closed sets.\nFor schemes one asks more: the map must stay closed even after one adds extra parameters to the base.\nThe map from the affine line to a point is closed, since the image of anything is the point or empty.\nAfter one adds a parameter, it becomes the projection of the plane to a line.\nThis projection sends the hyperbola $xy = 1$ onto the line with the origin removed, which is not closed.\nSo the affine line is not universally closed over a point, which reflects the missing point at infinity.\n",
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