A note on directly ordered subspaces of ℝn

Jennifer Del Valle; Piotr J. Wojciechowski

doi:10.2478/v10127-012-0031-y

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A note on directly ordered subspaces of ℝn

Tatra Mountains Mathematical Publications

Volume 52 (2012): Issue 1 (August 2012)

By: Jennifer Del Valle and Piotr J. Wojciechowski

Open Access

|Nov 2012

Abstract

A comprehensive method of determining if a subspace of usually ordered space Rn is directly-ordered is presented here. Also, it is proven in an elementary way that if a directly-ordered vector space has a positive cone generated by its extreme vectors then the Riesz Decomposition Property implies the lattice conditions. In particular, every directly-ordered subspace of Rn is a lattice- subspace if and only if it satisfies the Riesz Decomposition Property.

References

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Articles in this issue

DOI: https://doi.org/10.2478/v10127-012-0031-y | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 101 - 113

Published on: Nov 19, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

ordered vector space,

Related subjects:

© 2012 Jennifer Del Valle, Piotr J. Wojciechowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 52 (2012): Issue 1 (August 2012)