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Some unpublished papers
In paper 1 I extend a
theorem of Beckman and Quarles. I prove that a function mapping a normed
plane into itself in such a way that any two points with distance 1 is mapped
on two points with distance 1, is an isometry,
except if the geometry is quadrangular, i.e. except if the set of points with
norm 1 is a parallelogram. Paper 2 is described in
the section on unit distance graphs. . Documents: |