Normed Linear Spaces, Ausgabe 21,Teil 1

AB)-lattice AL)-space Amer b₁ Banach space boundedly complete Cauchy closed linear subspace closure co(S co(w completely regular cone conjugate space contains continuous functions convergent convex hull convex set convex subset Corollary countable defined Definition element equivalent exists extreme points f₁ factor space finite subset finite-dimensional Hahn-Banach theorem Hausdorff space Hence homeomorphic hyperplane implies inner-product space interior point isometry isomorphic L₁ l¹(w Lemma linear function linear isometry linear subspace linear topological space linearly independent locally convex Math maximal metric space minimal facet monotone N₁ non-empty normed linear space normed space pre-norm Proof properties prove real numbers reflexive rotund S₁ satisfies sequence set of extreme shows sublinear symmetric T₁ topological space topology totally bounded uniformly unit ball unordered vector lattice w-compact w*-closed w*-convergent w*-topology weakly wedge x₁ zero ηξω