nLab
Ostrowski's theorem

Contents

Statement

Theorem

(Alexander 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.

Theorem

(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.

References

In the course notes

Ostrowki’s theorem is discussed around p. 23.

Revised on July 18, 2014 01:49:40 by Urs Schreiber (31.160.36.246)