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DF-space

In the mathematical field of functional analysis, DF-spaces, also written (DF)-spaces are locally convex topological vector space having a property that is shared by locally convex metrizable topological vector spaces. They play a considerable part in the theory of topological tensor products.

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Overview

Definition

Properties

Sufficient conditions

Bibliography

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Map overview Semantic statistics

DF-space

Nodes37
Edges36
Triples30
Avg. degree1.95
Density0.054054
Components1

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DF-space

Top relations

related to Properties · 12
DF-space → Consequently, Every, Fréchet, If, Let, LM-space, Montel, Montel DF-space, Suppose, The, Then, Urysohn
related to Sufficient conditions · 10
DF-space → An, DF-spaces, Every, Every Banach, Every Hausdorff, From, Fréchet, Suppose, The, Then
is a · 3
DF-space → DF-space.The completion of a DF-space is a DF-space.The locally convex sum of a sequence of DF-spaces is a DF-space.An inductive limit of a sequence of DF-spaces is a DF-space.S…, Fréchet space.Every infinite-dimensional Montel DF-space is a sequential space but not a Fréchet, strong dual of some metrizable locally convex space
related to Examples · 3
DF-space → DF-spaces, There, TVS-isomorphic
related to Definition · 2
DF-space → DF, TVS

Important terminology Word statistics

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Important terminology

space convex displaystyle every locally spaces df-spaces metrizable topological vector sequence bounded nuclear oclc strong dual complete isbn tensor grothendieck

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
DF-spaceis aFréchet space.Every infinite-dimensional Montel DF-space is a sequential space but not a Fréchet0.90text
DF-spaceis astrong dual of some metrizable locally convex space0.90text
DF-spaceis aDF-space.The completion of a DF-space is a DF-space.The locally convex sum of a sequence of DF-spaces is a DF-space.An inductive limit of a sequence of DF-spaces is a DF-space.S…0.90text
DF-spacerelated to DefinitionTVS0.60section
DF-spacerelated to DefinitionDF0.60section
DF-spacerelated to ExamplesThere0.60section
DF-spacerelated to ExamplesDF-spaces0.60section
DF-spacerelated to ExamplesTVS-isomorphic0.60section
DF-spacerelated to PropertiesLet0.60section
DF-spacerelated to PropertiesThen0.60section
DF-spacerelated to PropertiesConsequently0.60section
DF-spacerelated to PropertiesThe0.60section

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    Min side: 3
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