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Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 2 / 01 June 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 434-441
- Print publication:
- 01 June 2013
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- Article
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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.
