Editing Seminorm (section)

{{Short description|Mathematical function}}
In [[mathematics]], particularly in [[functional analysis]], a '''seminorm''' is like a [[Norm (mathematics)|norm]] but need not be [[positive definite]].  Seminorms are intimately connected with [[convex set]]s: every seminorm is the [[Minkowski functional]] of some [[Absorbing set|absorbing]] [[Absolutely convex set|disk]] and, conversely, the Minkowski functional of any such set is a seminorm.

A [[topological vector space]] is locally convex if and only if its topology is induced by a family of seminorms.