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Line 103: If <math>B</math> is a bounded neighborhood of the origin in a (locally bounded) TVS then its image under any continuous linear map will be a bounded set. Consequently, a linear map from a locally bounded TVS into any other TVS is continuous if and only if it is bounded on a neighborhood. ~~Thus~~In particular, when the ___domain or codomain of a linear map is normable or seminormable, then continuity is equivalent to being bounded on a neighborhood. ==Continuous linear functionals==

Continuous linear operator: Difference between revisions