Barrelled set

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In functional analysis and related areas of mathematics a barrelled set or a barrel in a topological vector space is a set which is convex, balanced, absorbing and closed.

[edit] Examples

• In a semi normed vector space the unit ball is a barrel.
• Every locally convex topological vector space has a neighbourhood basis consisting of barrelled sets.

[edit] See also

• Barrelled space, a topological vector space where every barrelled set is a neighbourhood