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Closed graph theorem

In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions when functions with closed graphs are necessarily continuous.

Products, Graphs and maps with closed graphs & Closed graph theorem in point-set topology

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Graphs and maps with closed graphs

Topological spacesClosed subsetProduct topologyHausdorff space§ Closed graph theorem in point-set topology
7 related topics

Closed graph theorem in point-set topology

Point-set topologyContinuousCompactClosed linear operatorsUpper hemicontinuous
5 related topics

In functional analysis

Topological vector spacesF-spacesBanach spacesOpen mapping theorem
4 related topics

Relation to the open mapping theorem

Open mapping theorems
1 related topics

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Graphs and maps with closed graphs

Closed graph theorem in point-set topology

In functional analysis

Relation to the open mapping theorem

Bibliography

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Closed graph theorem

Nodes52
Edges51
Triples118
Avg. degree1.96
Density0.038462
Components1

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Closed graph theorem

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related to Bibliography · 82
Closed graph theorem → Albert, Applied Mathematics, Beckenstein, Berlin New York, Boca Raton, Bourbaki, Business Media, Chapters, Constantin, Convex Analysis, CRC Press, Distributions, Dover Publications, Edward, Eggleston, FL, Folland, François, Functional Analysis, Garling
see also · 10
Closed graph theorem → Almost, Condition, Fixed-point, Generalization, Linear, Map, Property, Space, Theorem, Type
related to Closed graph theorem in point-set topology · 7
Closed graph theorem → Closed, Hausdorff, Hausdorffness, If, In, Note, The
related to Graphs and maps with closed graphs · 6
Closed graph theorem → Any, Closed, Gamma, Hausdorff, If, It
related to Relation to the open mapping theorem · 6
Closed graph theorem → Gamma, Let, Now, Often, So, Then
related to For set-valued functions · 3
Closed graph theorem → Closed, For, Hausdorff
related to In functional analysis · 3
Closed graph theorem → If, The, TVSs
is a · 1
Closed graph theorem → important result in functional analysis that guarantees that a closed linear operator is continuous under certain conditions

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Important terminology

displaystyle closed graph continuous open spaces isbn theorem oclc topological hausdorff vector map times topology linear analysis functions graphs mapping

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SubjectPredicateObjectConfidenceSrc
Closed graph theoremis aimportant result in functional analysis that guarantees that a closed linear operator is continuous under certain conditions0.90text
Closed graph theoremrelated to BibliographyBourbaki0.60section
Closed graph theoremrelated to BibliographyNicolas0.60section
Closed graph theoremrelated to BibliographyTopological Vector Spaces0.60section
Closed graph theoremrelated to BibliographyChapters0.60section
Closed graph theoremrelated to BibliographyTranslated0.60section
Closed graph theoremrelated to BibliographyEggleston0.60section
Closed graph theoremrelated to BibliographyMadan0.60section
Closed graph theoremrelated to BibliographyBerlin New York0.60section
Closed graph theoremrelated to BibliographySpringer-Verlag0.60section
Closed graph theoremrelated to BibliographyISBN0.60section
Closed graph theoremrelated to BibliographyOCLC0.60section

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