Topological vector space

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Definition

Continuous functions Product topology Topological group Walter Rudin T1

37 related topics

Topological structure

Abelian group Completely regular Normal Quotient topology Convex

32 related topics

Types

Closed graph theorem Open mapping theorem F-spaces Complete L 1 {\displaystyle L^{1}}

30 related topics

Properties

Convex hull Convex combinations Linear combinations Connected Locally connected

24 related topics

Topics to explore

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Examples

Linear maps

Hyperplane
Linear functional
Kernel Kernel (algebra)
Closed Closed set

Types

Closed graph theorem
Open mapping theorem Open mapping theorem (functional analysis)
F-spaces F-space
Complete Complete space
L 1 {\displaystyle L^{1}} Lp space
Local base
Minkowski functionals Minkowski functional
Hahn–Banach theorem
Banach–Steinhaus theorem
Bornological space
Continuous linear operators Continuous linear operator
Bounded linear operators Bounded linear operator
Stereotype space
Reflexive Banach spaces Reflexive space
Compact Compact set
Fréchet spaces Fréchet space
LF-spaces LF-space
Limits Limit (category theory)
ILH spaces ILH space?action=edit&redlink=1
Inverse limits Inverse limit
Nuclear spaces Nuclear space
Nuclear operator
Normed spaces Normed space
Norm Norm (mathematics)
Seminorm Seminorm (mathematics)?action=edit&redlink=1
Functions of bounded variation Bounded variation
Certain spaces Ba space
Inner product
Hardy spaces Hardy space
Euclidean spaces Euclidean space

Dual space

Properties

Convex hull
Convex combinations Convex combination
Linear combinations Linear combination
Connected Connected space
Locally connected Locally connected space
Arcwise connected
Sublinear functional
Second category
Nonmeager space
Topological interior
Subspace Topological subspace
"tube" Tube lemma
Quotient map
Closed map Open and closed maps
Topological complement Complemented subspace
Indiscrete topology
Nowhere dense
Baire space
Nonmeager
Convex balanced hull
Balanced hull
F-seminorms F-seminorm
Predicate Predicate (mathematical logic)
(Minkowski) sum Minkowski sum

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Map overview Semantic statistics

Nodes186

Edges185

Triples192

Avg. degree1.99

Density0.010753

Components1

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Topological vector space

Top relations

related to Further reading · 91

Topological vector space → Addison-Wesley, Addison-Wesley Publishing Co, Addison-Wesley Publishing Company, Alex, Alexander, Amsterdam New York, An Introduction, Applications, Berlin New York, Bierstedt, Birkhäuser Basel, Bourbaki, Breach Science Publishers, Business Media, Cambridge England, Cambridge Tracts, Cambridge University Press, Chaljub, Cham, Chapters

related to Completeness and uniform structure · 13

Topological vector space → But, Cauchy, Every TVS, Hausdorff, Hausdorff TVS, Hausdorff TVSs, However, The, Therefore, This, TVS, TVSs, Tychonoff

related to Finite-dimensional spaces · 9

Topological vector space → By, Euclidean, Hausdorff, If, Let, Riesz's, This, This Hausdorff, TVS-isomorphic

related to Non-Hausdorff spaces and the closure of the origin · 9

Topological vector space → Because, Every, Hausdorff, If, In, The, This, Thus, TVS

see also · 9

Topological vector space → Algebraic, Area, Banach, Group, Normed, Space, Subject, Type, Vector

related to Cartesian products · 8

Topological vector space → Cartesian, Consider, Euclidean, Hausdorff, The, This, This TVS, With

related to Non-normed spaces · 8

Topological vector space → An, Examples, Kolmogorov's, Montel, Schwartz, The, There, These

related to Topological structure · 8

Topological vector space → Every TVS, Given, Hausdorff, Hence, Let, This, TVS, X/M

related to Dual space · 7

Topological vector space → Alaoglu, Banach, Caution, Every, However, This, Whenever

related to Metrizability · 5

Topological vector space → Birkhoff, If, Kakutani, The, There

Important terminology Word statistics

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Important terminology

displaystyle vector space topology topological convex tvs every closed spaces hausdorff mathbb set operatorname neighborhood subseteq bounded cl compact subset

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Topological vector space	is a	vector space that is also a topological space with the property that the vector space operations	0.90	text
Topological vector space	is a	abelian topological group	0.90	text
completeness	instance of	Therefore making sense to related notions	0.80	text
uniform convergence	instance of	Therefore making sense to related notions	0.80	text
Cauchy nets	instance of	Therefore making sense to related notions	0.80	text
and uniform continuity	instance of	Therefore making sense to related notions	0.80	text
etc.	instance of	Therefore making sense to related notions	0.80	text
which are always assumed to be with respect to this uniformity	instance of	Therefore making sense to related notions	0.80	text
Topological vector space	related to Cartesian products	Cartesian	0.60	section
Topological vector space	related to Cartesian products	Consider	0.60	section
Topological vector space	related to Cartesian products	Euclidean	0.60	section
Topological vector space	related to Cartesian products	This	0.60	section

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Definition

Topological structure

Types

Properties

Key facts & relationships

Topics to explore

Overview

Motivation

Definition

Topological structure

Examples

Linear maps

Types

Dual space

Properties

Advanced semantic analysis

Map overview Semantic statistics

Topological vector space

How this topic connects Entity context

Topological vector space

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges