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# Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces

Published:2011-08-03
Printed: Jun 2013
• Witold Wnuk,
Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland
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## Abstract

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 property