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Some Remarks on the Algebraic Sum of Ideals and Riesz Subspaces

Published online by Cambridge University Press:  20 November 2018

Witold Wnuk
Witold Wnuk*
Affiliation:
Faculty of Mathematics and Computer Science, A.Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland e-mail: wnukwit@amu.edu.pl
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Abstract.

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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.

Keywords

46A4046B4246B45locally solid Riesz spaceRiesz subspaceidealminimal topological vector spaceLebesgue property

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 2 , 01 June 2013 , pp. 434 - 441
Copyright
Copyright © Canadian Mathematical Society 2013

References

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