Discontinuous linear map

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Role of the axiom of choice

Banach spaces ZFC Set theory Robert M. Solovay Model

11 related topics

A nonconstructive example

Real numbers Rationals Hamel basis Noncommensurable Measurable

7 related topics

A concrete example

Smooth functions Uniform norm Derivative Linear functional Dual space

6 related topics

Beyond normed spaces

Hahn–Banach theorem Minkowski gauge L p ( R , d x ) {\displaystyle L^{p}(\mathbb {R} ,dx)}Lebesgue measure Quasinorm

6 related topics

Topics to explore

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Overview

Mathematics
Linear maps Linear map
Functions Function (mathematics)
Linear spaces Linear space
Linear approximation
Topological spaces Topological space
Topological vector spaces Topological vector space
Continuous Continuous map
Dimensional Dimension (linear algebra)
Normed spaces Normed space
Complete Complete space
Axiom of choice

A linear map from a finite-dimensional space is always continuous

Finite-dimensional
Triangle inequality
Any two norms on a finite-dimensional space are equivalent Norm (mathematics)
Bounded linear operator
Supremum

A concrete example

A nonconstructive example

Real numbers Real number
Rationals
Hamel basis
Noncommensurable Commensurability (mathematics)
Measurable Measurable function
Additive Additive map
Vitali set

General existence theorem

Role of the axiom of choice

Banach spaces Banach space
ZFC
Set theory
Robert M. Solovay
Model Model (model theory)
Constructivism Constructivism (mathematics)
DC Dependent choice
Baire property
Garnir–Wright closed graph theorem Garnir–Wright closed graph theorem?action=edit&redlink=1
F-space
Ceitin's theorem Ceitin's theorem?action=edit&redlink=1

Closed operators

Closed graph theorem
Densely defined operators Densely defined operator
Polynomial functions Polynomial function
Stone–Weierstrass theorem
Nowhere continuous function

Beyond normed spaces

Hahn–Banach theorem
Minkowski gauge
L p ( R , d x ) {\displaystyle L^{p}(\mathbb {R} ,dx)} Lp space
Lebesgue measure
Quasinorm
Groups Group (mathematics)

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Map overview Semantic statistics

Nodes64

Edges63

Triples48

Avg. degree1.97

Density0.03125

Components1

How this topic connects Entity context

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Discontinuous linear map

Top relations

related to Beyond normed spaces · 12

Discontinuous linear map → Another, Banach, Fréchet, Hahn, In, Lebesgue, Minkowski, Note, On, The, There, This

related to A nonconstructive example · 10

Discontinuous linear map → An, By, Hamel, Let, Note, One, The, Then, This, Vitali

related to Role of the axiom of choice · 10

Discontinuous linear map → AC, As, Banach, Clearly AC, In, On, Robert, Solovay, This, ZFC

related to General existence theorem · 8

Discontinuous linear map → Assume, Complete, Discontinuous, For, If, Let, Then, We

related to A concrete example · 7

Discontinuous linear map → Cauchy, Examples, For, In, Indeed, The, This

Important terminology Word statistics

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Important terminology

linear displaystyle spaces space continuous discontinuous maps map complete infinite-dimensional normed vector example operators existence choice closed operator theorem axiom

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
the derivative can succeed in defining a discontinuous linear map everywhere on a complete space	instance of	no concrete construction	0.80	text
Discontinuous linear map	related to A concrete example	Examples	0.60	section
Discontinuous linear map	related to A concrete example	Cauchy	0.60	section
Discontinuous linear map	related to A concrete example	In	0.60	section
Discontinuous linear map	related to A concrete example	For	0.60	section
Discontinuous linear map	related to A concrete example	The	0.60	section
Discontinuous linear map	related to A concrete example	Indeed	0.60	section
Discontinuous linear map	related to A concrete example	This	0.60	section
Discontinuous linear map	related to A nonconstructive example	An	0.60	section
Discontinuous linear map	related to A nonconstructive example	Hamel	0.60	section
Discontinuous linear map	related to A nonconstructive example	Note	0.60	section
Discontinuous linear map	related to A nonconstructive example	One	0.60	section

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Min side: 3

Research this topic

Explore this topic

Role of the axiom of choice

A nonconstructive example

A concrete example

Beyond normed spaces

Key facts & relationships

Topics to explore

Overview

A linear map from a finite-dimensional space is always continuous

A concrete example

A nonconstructive example

General existence theorem

Role of the axiom of choice

Closed operators

Beyond normed spaces

Advanced semantic analysis

Map overview Semantic statistics

Discontinuous linear map

How this topic connects Entity context

Discontinuous linear map

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