Editing Local field (section)

==Induced absolute value==

Given such an absolute value on a field ''K'', the following topology can be defined on ''K'': for a positive real number ''m'', define the subset ''B''<sub>m</sub> of ''K'' by
:<math>B_m:=\{ a\in K:|a|\leq m\}.</math>
Then, the ''b+B''<sub>m</sub> make up a [[neighbourhood basis]] of b in ''K''.

Conversely, a topological field with a non-discrete locally compact topology has an absolute value defining its topology. It can be constructed using the [[Haar measure]] of the [[Field (mathematics)#Related algebraic structures|additive group]] of the field.