nLab
Ostrowski's theorem

Context

Analysis

Algebra

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.

Last revised on July 18, 2014 at 01:49:40. See the history of this page for a list of all contributions to it.