Topological vector spaces

Barrelled space

In functional analysis and related areas of mathematics, a barrelled space (also written barreled space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood for the zero vector. A barrelled set or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach–Steinhaus theorem still holds for them. Barrelled spaces were introduced by Bourbaki. (Wikipedia).

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Metrizable topological vector space | Almost open map | Functional analysis | F-space | Barrelled set | Bornivorous set | Dual system | Quasibarrelled space | Normed vector space | Nowhere dense set | Quasi-complete space | Topological vector space | Absorbing set | Banach space | Countably quasi-barrelled space | Baire space | Strong dual space | Hausdorff space | Absolutely convex set | Seminorm | Neighbourhood (mathematics) | Reflexive space | Continuous linear operator | Fréchet space | Mathematics | Set (mathematics) | Polar set | Locally convex topological vector space | Hilbert space | Balanced set | Infrabarrelled space | Lp space | Closed graph theorem | Montel space | Complete topological vector space | Sequentially complete | Convex set | Closed set