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

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Consequences of the Hahn-Banach theorems Proof. Remember that M is equipped with the relative topology inherited from X. Since f : M → Φ is continuous with respect to this topology, M0 = f −1 ({0}) is closed in that topology. This means that M\M0 = M ∩ W for some open set W of X. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Consequences of the Hahn-Banach theorems Proof. Remember that M is equipped with the relative topology inherited from X. Since f : M → Φ is continuous with respect to this topology, M0 = f −1 ({0}) is closed in that topology. This means that M\M0 = M ∩ W for some open set W of X. Then W ∩ M0 = W ∩ M ∩ M0 = (M\M0) ∩ M0 = ∅. 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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