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

Every seminorm is a sublinear function, and thus satisfies all properties of a sublinear function, including convexity, $${\displaystyle p(0)=0,}$$ and for all vectors $${\displaystyle x,y\in X}$$: the reverse triangle inequality:
For any vector See more

The concept of norm in composition algebras does not share the usual properties of a norm.
A composition algebra See more

• Asymmetric norm – Generalization of the concept of a norm
• Banach space – Normed vector space that is complete
• Contraction mapping – Function reducing distance between all points See more

Let $${\displaystyle X}$$ be a vector space over either the real numbers $${\displaystyle \mathbb {R} }$$ or the complex numbers $${\displaystyle \mathbb {C} .}$$ See more

• The trivial seminorm on $${\displaystyle X,}$$ which refers to the constant $${\displaystyle 0}$$ map on $${\displaystyle X,}$$ induces the indiscrete topology on $${\displaystyle X.}$$
• Let See more

Pseudometrics and the induced topology
A seminorm $${\displaystyle p}$$ on $${\displaystyle X}$$ induces a topology, called the seminorm-induced topology, via the canonical See more