Functional analysis Topological vector spaces: basic notions Concept
Barrelled space
Summary
A barrel is a closed, convex, balanced and absorbing set. A barrelled space is a locally convex space in which every barrel is a neighbourhood of . Barrelled spaces are the spaces where the uniform boundedness principle (Banach–Steinhaus theorem) holds in its usual form. Banach spaces, Fréchet spaces and LF-spaces are barrelled.
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| Tag | ZE6DXEJB8H |
|---|---|
| URI | m2://ZE6DXEJB8H |
| Kind | concept |
| Writing | W0 stub |
| MSC | 46A08 |
| Specializes | Locally convex space |
| Same as | |
| Changed | 2 November 2026 |
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