Multiplicative distance

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

• $\mu (AB)>1.$
• AB is congruent to A'B' iff $\mu (AB)=\mu (A^{\prime }{B}^{\prime }).$
• AB < A'B' iff $\mu (AB)<\mu (A^{\prime }{B}^{\prime }).$
• $\mu (AB+CD)=\mu (AB)\mu (CD).$

See also

• Algebraic geometry
• Hyperbolic geometry
• Poincaré disc model
• Hilbert's arithmetic of ends