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Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces
Published online by Cambridge University Press: 20 November 2018
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, $I\,\bigcap \,G\,=\,\left\{ 0 \right\}$, and $I\,+\,G$ is not closed.
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- Copyright © Canadian Mathematical Society 2013
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