Geodesic
Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 434-441

Voir la notice de l'article provenant de la source Cambridge University Press

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, $I\,\bigcap \,G\,=\,\left\{ 0 \right\}$ , and $I\,+\,G$ is not closed.
DOI : 10.4153/CMB-2011-151-0
Mots-clés : 46A40, 46B42, 46B45, locally solid Riesz space, Riesz subspace, ideal, minimal topological vector space, Lebesgue property 
Wnuk, Witold. Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 434-441. doi: 10.4153/CMB-2011-151-0
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