Title
A note on directly ordered subspaces of ℝn
Publication Date
1-1-2012
Document Type
Article
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.
COinS
Comments
Del Valle, J., & Wojciechowski, P. J. (2012). A note on directly ordered subspaces of ℝn, Tatra Mountains Mathematical Publications, 52(1), 101-113. doi: https://doi.org/10.2478/v10127-012-0031-y