Normed Linear Spaces, Issue 21, Part 1 |
Contents
Linear spaces | 1 |
Normed Linear spaces | 24 |
Completeness compactness and reflexivity | 44 |
Copyright | |
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a₁ AL)-space Amer b₁ Banach space boundedly complete Cauchy closed linear subspace closure co(S co(w completely regular conjugate space contains continuous functions convergent convex hull convex set Corollary countable defined Definition element equivalent exists extreme points f₁ factor space finite subset finite-dimensional H₁ Hahn-Banach theorem Hausdorff space Hence homeomorphic hyperplane implies inner-product space interior point isometry isomorphic L₁ Lemma linear function linear isometry linear subspace linear topological space linearly independent locally convex mapping Math maximal metric space minimal facet monotone N₁ non-empty normed linear space normed space Proof properties prove reflexive rotund S₁ satisfies sequence set of extreme shows sublinear sublinear functional symmetric t₁ topological space topology totally bounded U₁ unit ball vector lattice w-compact w*-closed w*-topology weakly wedge x₁ ηεω ίξω κεμ κεω ΠΕΔ