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.
- Fréchet spaces, and in particular Banach spaces, are barrelled, but generally a normed vector space is not barrelled.
- Montel spaces are barrelled. Consequently, strong duals of Montel spaces are barrelled (since they are Montel spaces).
- locally convex spaces which are Baire spaces are barrelled.
- a separated, complete Mackey space is barrelled.
Read more about this topic: Barrelled Space
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