On the algebraic dimension of Riesz spaces

N. M. Baziv; O. B. Hrybel

doi:10.30970/ms.56.1.67-71

N. M. Baziv Vasyl Stefanyk Precarpathian National University
O. B. Hrybel Vasyl Stefanyk Precarpathian National University

DOI: https://doi.org/10.30970/ms.56.1.67-71

Keywords: Riesz space;, algebraic dimension;, lateral order

Abstract

We prove that the algebraic dimension of an infinite dimensional $C$-$\sigma$-complete Riesz space (in particular, of a Dedekind $\sigma$-complete and a laterally $\sigma$-complete Riesz space) with the principal projection property which either has a weak order unit or is not purely atomic, is at least continuum. A similar (incomparable to ours) result for complete metric linear spaces is well known.

Author Biographies

N. M. Baziv, Vasyl Stefanyk Precarpathian National University

Vasyl Stefanyk Precarpathian National University

O. B. Hrybel, Vasyl Stefanyk Precarpathian National University

Vasyl Stefanyk Precarpathian National University

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