Metrizability of totally ordered groups of infinite rank and their completions

被引：3

作者：

Olivos, E. ^{[1
]}

Soto, H. ^{[1
]}

Mansilla, A. ^{[1
]}

机构：

[1] Univ La Frontera, Dept Matemat & Estadist, Temuco, Chile

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2007年 / 14卷 / 05期

关键词：

metrizability; topological ordered groups; topological G-modules;

D O I：

10.36045/bbms/1197908907

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In [4], Ochsenius and Schikhof ask the following question. Given a totally ordered group G with a cofinal sequence, if every element of its Dedekind completion G(#) is the supremum of a sequence in G, does it follow that G(#) is metrizable? We answer their question by studying topological properties of a family of totally ordered groups, Gamma(alpha), and their completions Gamma(#)(alpha). Further-more we obtain for this family conditions both necessary and sufficient for the metrizability of Gamma(#)(alpha).

引用

页码：969 / 977

页数：9