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A note on existence of nontrivial continuous linear functional on TVS. (English) Zbl 1093.46500

Summary: We give a sufficient and necessary condition for the existence of non-trivial continuous linear functionals on topological vector spaces, and show that there is no nontrivial continuous linear functional on any quasi-bounded topological vector space.

MSC:

46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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