Locally compact field

In algebra, a locally compact field is a topological field whose topology forms a locally compact Hausdorff space.^[1] These kinds of fields were originally introduced in p-adic analysis since the fields ${\displaystyle \mathbb {Q} _{p}}$ are locally compact topological spaces constructed from the norm ${\displaystyle |\cdot |_{p}}$ on ${\displaystyle \mathbb {Q} }$. The topology (and metric space structure) is essential because it allows one to construct analogues of algebraic number fields in the p-adic context.