Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces

Canadian mathematical bulletin

Witold Wnuk¹ 

[1] Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

关键词: locally solid Riesz space;    Riesz subspace;    ideal;    minimal topological vector space;    Lebesgue property;   

DOI  :  10.4153/CMB-2011-151-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 locallysolid Riesz space and $I$ does not contain any order copy of $mathbb R^{mathbb N}$ then there exists aclosed, separable, discrete Riesz subspace $G$ such that the topology induced on $G$ is Lebesgue, $I cap G ={0}$, and $I + G$ is not closed.

【 授权许可】

Unknown