Ostrowski's theorem

**(Ostrowski)**

Any non-trivial absolute value on the rational numbers is equivalent either to the standard real absolute value, or to the p-adic absolute value.

**(Ostrowski)**

Any complete archimedean valued field is, as an associative algebra and as a topological space, isomorphic to either the real numbers or the complex numbers.

In the course notes

- Frédéric Paugam,
*Global analytic geometry and the functional equation*(2010) (pdf)

Ostrowki’s theorem is discussed around p. 23.

Revised on January 9, 2012 01:28:42
by Urs Schreiber
(82.113.119.184)