Definition of Seminorms. Meaning of Seminorms. Synonyms of Seminorms

- 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...
- continuous seminorms on X {\displaystyle X} , then P {\displaystyle {\mathcal {P}}} is called a base of continuous seminorms if it is a base of seminorms for...
- Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves...
- in particular, every norm is also a seminorm (and thus also a sublinear functional). However, there exist seminorms that are not norms. Properties (1.)...
- is complete with respect to the family of seminorms. A family P {\displaystyle {\mathcal {P}}} of seminorms on X {\displaystyle X} yields a Hausdorff...
- of (continuous) seminorms. The topology of X {\displaystyle X} is induced by a countable increasing sequence of (continuous) seminorms ( p i ) i = 1 ∞...
- Minkowski functional (which will necessarily be a seminorm). These relationships between seminorms, Minkowski functionals, and absorbing disks is a major...
- that it gives rise to a seminorm rather than a vector space norm. The quotient of this space by the kernel of this seminorm is also required to be a...
- {\displaystyle D.} Hahn–Banach theorem for seminorms — If p : M → R {\displaystyle p:M\to \mathbb {R} } is a seminorm defined on a vector subspace M {\displaystyle...
- all locally convex, which implies that they are defined by a family of seminorms. In analysis, a topology is called strong if it has many open sets and...