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ORDERED LINEAR SPACES
LINEAR LATTICES AND RIESZ SPACES
ORDERED TOPOLOGICAL LINEAR SPACES
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absorbent set algebra Archimedean Banach space barrelled space bounded decomposition closure commutative group commutative lattice group contains converse convex set COROLLARY CS-closed denote exists f extremal element extreme point finite following statements given gives an open Hausdorff Hausdorff space Hence implies interior point lattice ordering Let f Let X,Y linear lattice linear subspace locally compact locally convex space locally convex topology locally order-convex locally solid M-space metrizable Minkowski functional monotonic linear functional monotonic linear mapping nearly directed neighbourhood non-zero normed linear space normed spaces open decomposition order-bound topology order-complete order-intervals order-unit order-unit norm ordered linear space positive cone positive wedge Proof real lattice homomorphisms result follows Riesz space self-allied with respect semi-algebra seminorm space with positive statements are equivalent subgroup sublattice Take theorem topological linear space upward-directed usual ordering well-based