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1. CMB 2011 (vol 56 pp. 434)

Wnuk, Witold
 Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces Following ideas used by Drewnowski and Wilansky we prove that if \$I\$ is an infinite dimensional and infinite codimensional closed ideal in a complete metrizable locally solid Riesz space and \$I\$ does not contain any order copy of \$\mathbb R^{\mathbb N}\$ then there exists a closed, separable, discrete Riesz subspace \$G\$ such that the topology induced on \$G\$ is Lebesgue, \$I \cap G = \{0\}\$, and \$I + G\$ is not closed. Keywords:locally solid Riesz space, Riesz subspace, ideal, minimal topological vector space, Lebesgue propertyCategories:46A40, 46B42, 46B45

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