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a-Dedekind arbitrary Archimedean assume Banach Boolean algebras bounded linear functional Burmester centre classes d'équivalence closure operators Communicated by Prof compact complete lattice contains continuous function convergence convex Corollary countable defined definition denote disjoint dual space element ensemble equations equivalent espaces exists finite following theorem formula g-Cauchy given Hausdorff Hausdorff space Hence holds homomorphism hypothesis implies interval inverse limit isomorphic Lemma Lie algebra log log Math MATHEMATICS matrix maximal norm closed norm complete normal integral normal subspace normed Riesz space Note VIII obtain ooro OOS'O open set order dense plane point q polynomial system proof of Theorem prove real number result Riesz space s-prime ideal seminorm sequence subset super Dedekind complete superatomic Suppose system of type Theorem théorème topology uniformly zero