nLab
Ostrowski's theorem

Contents

Statement

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.

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