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Apr 25, 2016 at 8:46 comment added Jochen Wengenroth In terms of Banach discs the question whether a space has a finer Banach topology has a trivial answer: This is so if and only if there is an absorbing Banach disc.
Apr 25, 2016 at 8:44 comment added Jochen Wengenroth Such bounded sets $B$ are called Banach discs and the inductive limit topology you mention is the associated ultrabornological topology.
Apr 24, 2016 at 19:01 history answered goleta CC BY-SA 3.0