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Normed vector space

In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V {\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R…

Products, Topological structure & Normable spaces

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Overview

Definition

Topological structure

Normable spaces

Linear maps and dual spaces

Normed spaces as quotient spaces of seminormed spaces

Finite product spaces

Bibliography

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Normed vector space

Nodes81
Edges80
Triples14
Avg. degree1.98
Density0.024691
Components1

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Normed vector space

Top relations

see also · 5
Normed vector space → Banach, Characterization, Concept, Mazur, Vector
related to Linear maps and dual spaces · 3
Normed vector space → All, The, Together
related to Topological structure · 3
Normed vector space → If, The, This
is a · 1
Normed vector space → vector space equipped with a norm

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Important terminology

vector displaystyle space norm normed spaces topology defined banach metric continuous topological cdot every normable linear seminormed seminorm mathbb called

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Normed vector spaceis avector space equipped with a norm0.90text
continuityinstance ofand allows the definition of notions0.80text
convergenceinstance ofand allows the definition of notions0.80text
Normed vector spacerelated to Linear maps and dual spacesThe0.60section
Normed vector spacerelated to Linear maps and dual spacesTogether0.60section
Normed vector spacerelated to Linear maps and dual spacesAll0.60section
Normed vector spacerelated to Topological structureIf0.60section
Normed vector spacerelated to Topological structureThis0.60section
Normed vector spacerelated to Topological structureThe0.60section
Normed vector spacesee alsoBanach0.60section
Normed vector spacesee alsoMazur0.60section
Normed vector spacesee alsoConcept0.60section

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    Min side: 3
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