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Topological Vector Spaces/Direct sums
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Topological Vector Spaces
Exercises
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Let
$E$
be a TVS. Prove that all finite-dimensional subspaces of
$E$
have a topological complement if and only if for every
$x\notin {\overline {\{0\}}}$
, there exists
$x'\in E'$
so that
$x'(x)\neq 0$
.