barrelled space meaning in Hindi

Examples

1. Every barrelled space is quasi-barrelled.
2. A topological vector space X for which every barrelled bornivorous set in the space is a neighbourhood of 0 is called a quasi-barrelled space, where a set is bornivorous if it absorbs all bounded subsets of X.
3. *If X is a barrelled space, then its topology coincides with the strong topology \ beta ( X, X') on X and with the Mackey topology on X generated by the pairing ( X, X').
4. Given a barrelled space " X " and a locally convex space " Y ", then any family of pointwise bounded continuous linear mappings from " X " to " Y " is equicontinuous ( even uniformly equicontinuous ).
5. :A linear operator from a barrelled space " X " to a Fr�chet space " Y " is continuous if and only if its graph is closed in the space " X " & times; " Y " equipped with the product topology.