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

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Weak vector space topologies Proof. Proof of Theorem 3.10. Almost by definition, the open sets in X ′ -topology are the sets that are unions of sets of the form l −1 1 (V1) ∩ l −2 2 (V2) ∩ · · · ∩ l −1 n (Vn), where each li ∈ X ′ and Vi is an open subset of the scalars Φ. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Weak vector space topologies Proof. Proof of Theorem 3.10. Almost by definition, the open sets in X ′ -topology are the sets that are unions of sets of the form l −1 1 (V1) ∩ l −2 2 (V2) ∩ · · · ∩ l −1 n (Vn), where each li ∈ X ′ and Vi is an open subset of the scalars Φ. To show that X is a topological vector space in the X ′ -topology we check first that the vector space operations are continuous. 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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