Multiplicative distance

In algebraic geometry, $μ$ is said to be a multiplicative distance function over a field if it satisfies

$μ (A B) > 1.$
AB is congruent to A'B' iff $μ (A B) = μ (A^{'} B^{'}) .$
AB < A'B' iff $μ (A B) < μ (A^{'} B^{'}) .$
$μ (A B + C D) = μ (A B) μ (C D) .$

See also

References

↑ Hartshorne, Robin (2000), Geometry: Euclid and beyond, Undergraduate Texts in Mathematics, New York: Springer-Verlag, p. 363, doi:10.1007/978-0-387-22676-7, ISBN 0-387-98650-2, MR 1761093.

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