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Line 107: In particular, a linear functional on a arbitrary TVS is continuous if and only if it is bounded on a neighborhood.{{sfn\|Wilansky\|2013\|pp=53-55}} ~~Thus~~So in summary, when the ___domain {{em\|or}} the codomain of a linear map is normable or seminormable, then continuity will be [[Logical equivalence\|equivalent]] to being bounded on a neighborhood. '''Guaranteeing that "bounded" implies "continuous"'''

Continuous linear operator: Difference between revisions