About: Closed graph theorem

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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.

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rdfs:label	Closed graph theorem (en) Teorema de la gràfica tancada (ca) Satz vom abgeschlossenen Graphen (de) Teorema de la gráfica cerrada (es) Théorème du graphe fermé (fr) Teorema del grafico chiuso (it) 닫힌 그래프 정리 (ko) 閉グラフ定理 (ja) Stelling van de gesloten grafiek (nl) Twierdzenie o wykresie domkniętym (pl) Teorema do gráfico fechado (pt) Satsen om den slutna grafen (sv) Теорема о замкнутом графике (ru) 閉圖像定理 (zh) Теорема Банаха про замкнений графік (uk)
rdfs:comment	Der Satz vom abgeschlossenen Graphen ist ein mathematischer Satz aus der Funktionalanalysis. (de) 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. (en) En análisis funcional, el teorema de la gráfica cerrada establece lo siguiente: Este teorema se demuestra usando el teorema de la función abierta, y es casi imprescindible para resolver ciertos problemas de análisis funcional que no se pueden resolver con técnicas menos avanzadas. (es) En mathématiques, le théorème du graphe fermé est un théorème d'analyse fonctionnelle qui donne une condition suffisante dans un certain cadre pour qu'une application linéaire soit continue. (fr) In matematica, il teorema del grafico chiuso è un risultato basilare in analisi funzionale che caratterizza gli operatori lineari continui tra spazi di Banach in termini del grafico dell'operatore. La dimostrazione del teorema del grafico chiuso fa uso del teorema della funzione aperta. (it) 일반위상수학에서 닫힌 그래프 정리(닫힌graph定理, 영어: closed graph theorem)는 하우스도르프 공간으로 가는 연속 함수의 그래프가 닫힌집합이라는 정리다. (ko) 数学の分野における閉グラフ定理（へいグラフていり、英語: closed graph theorem）とは、バナッハ空間の間の連続線形作用素を作用素のグラフに関して特徴付けるような、関数解析学における基本的な結果の一つである。 (ja) De stelling van de gesloten grafiek is een stelling uit de functionaalanalyse, een onderdeel van de wiskundige analyse. Ze kenmerkt continue lineaire afbeeldingen tussen banachruimten. (nl) Twierdzenie o wykresie domkniętym – jedno z podstawowych twierdzeń klasycznej analizy funkcjonalnej, charakteryzujące ciągłe przekształcenia liniowe między F-przestrzeniami, a więc w szczególności między przestrzeniami Banacha. (pl) Нехай X, Y — банахові простори над одним і тим же полем, L — підпростір простору X. Для того, щоб лінійний оператор був неперервним, необхідно і достатньо, щоб його графік був замкнений в декартовому добутку (якщо його розглядати як нормований простір). (uk) Satsen om den slutna grafen är ett grundläggande resultat inom funktionalanalysen som karakteriserar kontinuerliga linjära operatorer mellan två Banachrum med hjälp av deras grafer. (sv) Em matemática, o Teorema do gráfico fechado é um dos resultados fundamentais da análise funcional. Ele estabelece uma relação entre a continuidade de um operador linear e o fato de seu gráfico ser fechado. (pt) Теорема о замкнутом графике — важный результат функционального анализа, устанавливающий критерий ограниченности линейного оператора между банаховыми пространствами. (ru) 閉圖像定理是數學中泛函分析的一條定理。 (zh) En matemàtiques, concretament en anàlisi funcional, el teorema de la gràfica tancadaés un dels resultats bàsics. El seu enunciat és el següent: Si i són espais de Banach i és un operador lineal, aleshores és continu si i sols si la seva gràfica és un subconjunt tancat de , amb la topologia producte. La demostració habitual es basa en el teorema de l'aplicació oberta. (ca)
name	Theorem (en) Closed graph theorem (en) Closed graph theorem for set-valued functions (en)
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dcterms:subject	Theorems in functional analysis
Wikipage page ID	497834 (xsd:integer)
Wikipage revision ID	1121918362 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Upper hemicontinuous John Wiley & Sons Compact space Continuous function Theorems in functional analysis Mathematics General topology Closed graph Closed set Functional analysis Closed linear operator Banach space Topological vector space Hausdorff space Cubic function F-space Graph of a function Continuous function (topology) Euclidean topology Topological space Heaviside function Indiscrete topology Point-set topology
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