关于Riesz空间的代数维数

Q3 Mathematics

Matematychni Studii Pub Date : 2021-10-23 DOI:10.30970/ms.56.1.67-71

N. Baziv, O. B. Hrybel

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引用次数: 0

摘要

我们证明了具有弱阶单元或非纯原子的主投影性质的无穷维$C$-$\sigma$-完备Riesz空间（特别是Dedekind$\sigma$-完备和横向$\sigma-$-完备的Riesz空间）的代数维数至少是连续的。完备度量线性空间的一个类似（与我们的结果不可比较）的结果是众所周知的。

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On the algebraic dimension of Riesz spaces

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.

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来源期刊

Matematychni Studii Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal is devoted to research in all fields of mathematics.