7. Consequences of the Hahn-Banach theorems - Aarhus Universitet

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Consequences of the Hahn-Banach theorems Theorem (The corollary on p. 59) Let X be a locally convex topological vector space. Then X ∗ separates the points of X, i.e. when x = y in X there is a l ∈ X ∗ such that l(x) = l(y). Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Consequences of the Hahn-Banach theorems Theorem (The corollary on p. 59) Let X be a locally convex topological vector space. Then X ∗ separates the points of X, i.e. when x = y in X there is a l ∈ X ∗ such that l(x) = l(y). Proof. Apply the Hahn-Banach separation theorem, Theorem 3.4 b), with A = {x} and B = {y}. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
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7. Consequences of the Hahn-Banach theorems - Aarhus Universitet

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