Tags: #todo #todo/stub Refs: ?

Adeles

See profinite completion.

Issues with the product topology

Solved by taking the restricted direct product: Can also define as a colimit

Adele ring of a global field

For a global field, the adeles will always be locally compact Hausdorff, and hence admits a Haar measure.

Ideles

Warning: \({\mathbf{A}}_K^{\times}\) is not a topological group since inversion is not continuous.

Idele norms