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

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Weak vector space topologies Let X be a real or complex vector space, and M a collection of lineat functionals X → Φ. The sets of the form {y ∈ X : |l(y) − l(x)| < ǫ} (3) where x ∈ X,ǫ > 0 and l ∈ M vary, is a subbase for a topology on X, Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Weak vector space topologies Let X be a real or complex vector space, and M a collection of lineat functionals X → Φ. The sets of the form {y ∈ X : |l(y) − l(x)| < ǫ} (3) where x ∈ X,ǫ > 0 and l ∈ M vary, is a subbase for a topology on X, namely the topology where a subset of X is open if and only if it is the union of sets which are the intersection of a finite collection of such sets. Klaus Thomsen 7. Consequences of the Hahn-Banach theorems
Page 1 and 2: 7. Consequences of the Hahn-Banach
Page 3 and 4: We read in W. Rudin: Functional Ana
Page 5 and 6: Consequences of the Hahn-Banach the
Page 27: Weak vector space topologies Let X
Page 31 and 32: Weak vector space topologies Lemma
Page 37 and 38: Weak vector space topologies Proof.
Page 41 and 42: Weak vector space topologies Theore
Page 77: Weak vector space topologies Proof.

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

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