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Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.
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Extending affine maps defined on weakly closed sets to the whole topological space
Given $C$ a weakly closed convex subset of a (real) Banach space $B$, with $0\in C$ and $\varphi:C\longrightarrow \mathbb{R}$ weakly continuous, with $\varphi(0)=0$, can we extend $\varphi$ to a $\wid …