Definition of Seminorms. Meaning of Seminorms. Synonyms of Seminorms

Here you will find one or more explanations in English for the word Seminorms. Also in the bottom left of the page several parts of wikipedia pages related to the word Seminorms and, of course, Seminorms synonyms and on the right images related to the word Seminorms.

Definition of Seminorms

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Meaning of Seminorms from wikipedia

- 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...
- 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 ∞...
- {\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...
- Minkowski functional (which will necessarily be a seminorm). These relationships between seminorms, Minkowski functionals, and absorbing disks is a major...
- all seminorms p {\displaystyle p} ; it is sufficient to check it for a set of seminorms that generate the topology, in other words, a set of seminorms that...