Open AccessOn the algebraic dimension of Riesz spaces
Author(s) -
Nataliia Baziv,
O. B. Hrybel
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.56.1.67-71
Subject(s) - dedekind cut , mathematics , riesz representation theorem , pure mathematics , algebraic number , m. riesz extension theorem , dimension (graph theory) , projection (relational algebra) , sigma , space (punctuation) , mathematical analysis , physics , algorithm , quantum mechanics , linguistics , philosophy
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.