Ordered Topological Vector Spaces |
Contents
CONVERGENCE IN VECTOR LATTICES | 43 |
Intrinsic Topologies of Ordered Vector Spaces | 117 |
Selected Topics in the Theory of Ordered | 138 |
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A₁ Archimedean b₁ barreled space bounded sets Chapter complete vector lattice contains continuous linear functional continuous linear mappings converges to xo convex space ordered Corollary defined direct sum dual system element example finite following result Hausdorff space hence implies K₁ K₂ Köthe L-space lattice ideal lattice operations linear subspace locally convex lattice locally convex space locally convex topology Math metrizable neighborhood basis non-negative norm normal cone order bounded linear order bounded sets order complete vector order converges order interval order structure order topology ordered topological vector ordered vector space positive cone positive integer positive linear functional positive linear mapping Proof Proposition real numbers regularly ordered vector relatively uniformly convergent resp S-topology seminorms sequence space sequentially order continuous strict b-cone supremum T₁ Theorem topological vector lattice topological vector space uniform convergence vector space E(T x₁ y₁