About: Webbed space

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Space where open mapping and closed graph theorems hold

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dbo:description
  • space where open mapping and closed graph theorems hold (en)
  • estructura topológica en la que se cumplen los teoremas de la aplicación abierta y del grafo cerrado (es)
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dbp:mathStatement
  • Any continuous surjective linear map from a webbed locally convex space onto an ultrabornological space is open. (en)
  • Any continuous surjective linear map from a webbed locally convex space onto an inductive limit of Baire locally convex spaces is open. (en)
  • Let be a linear map between TVSs that is sequentially closed . If is a webbed space and is an ultrabornological space , then is continuous. (en)
  • A topological vector space is a Fréchet space if and only if it is both a webbed space and a Baire space. (en)
  • Any closed linear map from the inductive limit of Baire topological vector spaces into a webbed topological vector space is continuous. (en)
  • Any closed linear map from the inductive limit of Baire locally convex spaces into a webbed locally convex space is continuous. (en)
  • If the image of a closed linear operator from locally convex webbed space into Hausdorff locally convex space is nonmeager in then is a surjective open map. (en)
dbp:name
  • Theorem (en)
  • Closed Graph Theorem (en)
  • Open Mapping Theorem (en)
dbp:note
  • de Wilde 1978 (en)
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dct:subject
gold:hypernym
rdfs:label
  • Webbed space (en)
  • Raum mit Gewebe (de)
  • ウェブ付き空間 (ja)
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