What is Locally compact field?

In algebra, a locally compact field is a topological field whose topology forms a locally compact Hausdorff space. These kinds of fields were originally introduced in p-adic analysis since the fields Q p {\displaystyle \mathbb {Q} _{p}} are locally compact topological spaces constructed from the norm | ⋅ | p {\displaystyle |\cdot |_{p}} on Q {\displaystyle \mathbb {Q} }. The topology is essential because it allows one to construct analogues of algebraic number fields in the p-adic context.