Dual of a topological vector space. Is it nontrivial?
In the case of normed spaces we know their duals are nonempty using a
quick application of the Hahn Banach Theorem.
If we step back to the larger class of locally convex spaces, an
enthralling sequence of separation results yields another nontrivial dual.
What about general topological vector spaces? Is it possible to have a
nontrivial topological vector space over which every linear functional is
discontinuous?
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