Topological vector spaces

Ultrabornological space

In functional analysis, a topological vector space (TVS) is called ultrabornological if every bounded linear operator from into another TVS is necessarily continuous. A general version of the closed graph theorem holds for ultrabornological spaces. Ultrabornological spaces were introduced by Alexander Grothendieck (Grothendieck [1955, p. 17] "espace du type (β)"). (Wikipedia).

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Related pages

Nuclear space | Functional analysis | Bornivorous set | Alexander Grothendieck | Quasi-ultrabarrelled space | Topological vector space | Absorbing set | Barrelled space | Strong dual space | Minkowski functional | Absolutely convex set | Fréchet space | Schwartz topological vector space | Ultrabarrelled space | Bornological space | Balanced set | Closed graph theorem | Complete topological vector space | DF-space