EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A (X ⊕ X ) INTO A (X)

被引：2

作者：

Krupski, Mikolaj ^{[1
,2
]}

Leiderman, Arkady ^{[3
]}

Morris, Sidney ^{[4
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Univ Warsaw, Inst Math, Ul Banacha 2, PL-02097 Warsaw, Poland

[3] Ben Gurion Univ Negev, Dept Math, POB 653, Beer Sheva, Israel

[4] Federat Univ Australia, Sch Sci Engn & Informat Technol, POB 663, Ballarat, Vic 3353, Australia

来源：

MATHEMATIKA | 2019年 / 65卷 / 03期

关键词：

EQUIVALENT; SPACES;

D O I：

10.1112/S0025579319000123

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following question: for which metrizable separable spaces X does the free abelian topological group A (X circle plus X) isomorphically embed into A (X). While for many natural spaces X such an embedding exists, our main result shows that if X is a Cook continuum or X is a rigid Bernstein set, then A(X circle plus X) does not embed into A(X) as a topological subgroup. The analogous statement is true for the free boolean group B (X).

引用

页码：708 / 718

页数：11

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