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Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space can be characterized through the behaviour of its weakly- unconditionally Cauchy series in .
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