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- Open_mapping_theorem_(functional_analysis) abstract "In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely, (Rudin 1973, Theorem 2.11): Open Mapping Theorem. If X and Y are Banach spaces and A : X → Y is a surjective continuous linear operator, then A is an open map (i.e. if U is an open set in X, then A(U) is open in Y).The proof uses the Baire category theorem, and completeness of both X and Y is essential to the theorem. The statement of the theorem is no longer true if either space is just assumed to be a normed space, but is true if X and Y are taken to be Fréchet spaces.".
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- Open_mapping_theorem_(functional_analysis) wikiPageOutDegree "31".
- Open_mapping_theorem_(functional_analysis) wikiPageRevisionID "663007551".
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Academic_Press,_Inc..
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Baire_category_theorem.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Baires_category_theorem.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Banach_space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Bijection.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Bijective.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Bounded_inverse_theorem.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Bounded_linear_operator.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Bounded_operator.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Category:Articles_containing_proofs.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Category:Theorems_in_functional_analysis.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Cauchy_sequence.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Closed_graph_theorem.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Closed_set.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink F-space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Fréchet_space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Functional_analysis.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Inverse_function.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Isomorphism.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Juliusz_Schauder.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Kernel_(linear_algebra).
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Meager_set.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Meagre_set.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Normed_space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Normed_vector_space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Open_and_closed_maps.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Open_map.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Open_mapping_theorem_(complex_analysis).
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Open_set.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Quotient_space_(linear_algebra).
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Sequence.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Stefan_Banach.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Surjective.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Surjective_function.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Topological_vector_space.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Unit_ball.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLink Unit_sphere.
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLinkText "Open mapping theorem (functional analysis)".
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLinkText "Open mapping theorem".
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLinkText "The Open Mapping Theorem.".
- Open_mapping_theorem_(functional_analysis) wikiPageWikiLinkText "open mapping theorem".
- Open_mapping_theorem_(functional_analysis) hasPhotoCollection Open_mapping_theorem_(functional_analysis).
- Open_mapping_theorem_(functional_analysis) id "8537".
- Open_mapping_theorem_(functional_analysis) title "Proof of open mapping theorem".
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:Citation.
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:Functional_Analysis.
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:Harv.
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:Math.
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:PlanetMath_attribution.
- Open_mapping_theorem_(functional_analysis) wikiPageUsesTemplate Template:Reflist.
- Open_mapping_theorem_(functional_analysis) subject Category:Articles_containing_proofs.
- Open_mapping_theorem_(functional_analysis) subject Category:Theorems_in_functional_analysis.
- Open_mapping_theorem_(functional_analysis) hypernym Result.
- Open_mapping_theorem_(functional_analysis) comment "In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is surjective then it is an open map. More precisely, (Rudin 1973, Theorem 2.11): Open Mapping Theorem. If X and Y are Banach spaces and A : X → Y is a surjective continuous linear operator, then A is an open map (i.e.".
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