Multiplicative distance

In algebraic geometry, μ {\displaystyle \mu } is said to be a multiplicative distance function over a field if it satisfies[1]

  • μ ( A B ) > 1. {\displaystyle \mu (AB)>1.\,}
  • AB is congruent to A'B' iff μ ( A B ) = μ ( A ′ B ′ ) . {\displaystyle \mu (AB)=\mu (A'B').\,}
  • AB < A'B' iff μ ( A B ) < μ ( A ′ B ′ ) . {\displaystyle \mu (AB)<\mu (A'B').\,}
  • μ ( A B + C D ) = μ ( A B ) μ ( C D ) . {\displaystyle \mu (AB+CD)=\mu (AB)\mu (CD).\,}

See also

References

  1. ^ 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.


  • v
  • t
  • e