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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 absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm.

Art, Topologies of seminormed spaces & Definition

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Overview

Definition

Examples

Minkowski functionals and seminorms

Algebraic properties

Topologies of seminormed spaces

Generalizations

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Seminorm

Nodes67
Edges66
Triples54
Avg. degree1.97
Density0.029851
Components1

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Seminorm

Top relations

related to Examples · 12
Seminorm → Any, Every, For, However, If, In, It, Lebesgue, Let, Omega, The, To
related to Pseudometrics and the induced topology · 7
Seminorm → Equivalently, Every, Hausdorff, The, Then, This, X/W
related to Normability and seminormability · 6
Seminorm → Hausdorff, Kolmogorov's, Normability, T1, Thus, TVS
is a · 5
Seminorm → Minkowski functional of some absorbing disk and, norm if q, seminorm p, sublinear function, type of function called a sublinear function
related to Minkowski functionals and seminorms · 4
Seminorm → Conversely, Given, Minkowski, Seminorms
related to Definition · 3
Seminorm → Absolute, Let, Subadditivity/Triangle
related to Hahn–Banach theorem for seminorms · 3
Seminorm → Banach, Hahn, Seminorms
related to Inequalities involving seminorms · 3
Seminorm → If, Suppose, Then
related to Relationship to other norm-like concepts · 3
Seminorm → G-seminorm, Let, The
related to Topological properties · 3
Seminorm → If, The, TVS

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Important terminology

displaystyle vector space leq norm convex isbn oclc topological seminorms mathbb topology functional spaces sublinear function following every bounded linear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Seminormis aMinkowski functional of some absorbing disk and0.90text
Seminormis atype of function called a sublinear function0.90text
Seminormis asublinear function0.90text
Seminormis anorm if q0.90text
Seminormis aseminorm p0.90text
Seminormrelated to Algebraic propertiesEvery0.60section
Seminormrelated to Algebraic propertiesFor0.60section
Seminormrelated to Continuity of linear mapsIf0.60section
Seminormrelated to Continuity of seminormsIf0.60section
Seminormrelated to Continuity of seminormsThere0.60section
Seminormrelated to DefinitionLet0.60section
Seminormrelated to DefinitionSubadditivity/Triangle0.60section

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