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Tagged with affine-geometry mg.metric-geometry
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Line-preserving bijection of ${\mathbb{R}}^n$ onto itself
If $f:{\mathbb{R}}^n\to{\mathbb{R}}^n$ $(n\ge2)$ is a bijection such that the image of every line is a line (continuity of $f$ not assumed), must $f$ be an affinity?
Assuming continuity would ...