nLab Ostrowski's theorem

Contents

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

Discussion in point-free topology:

Last revised on December 12, 2023 at 20:20:04. See the history of this page for a list of all contributions to it.