Seminorm

In mathematics, particularly in functional analysis, a seminorm is like a norm but need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm is the Minkowski functional of some absorbingdisk 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.