On local quasi-convexity as a three-space property in topological abelian groups

被引：1

作者：

Dominguez, X. ^{[1
]}

Tarieladze, V ^{[2
]}

机构：

[1] Univ A Coruna, Dept Matemat, La Coruna, Spain

[2] Georgian Tech Univ, Muskhelishvili Inst Computat Math, Tbilisi, Georgia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 499卷 / 02期

基金：

美国国家科学基金会;

关键词：

Locally quasi-convex group; Three-space property; Dually embedded subgroup; Extension of topological abelian groups;

D O I：

10.1016/j.jmaa.2021.125052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a topological abelian group and H a subgroup of X. We find conditions under which local quasi-convexity of both H and X/H results in the same property for X. This is true for instance if H is precompact, or if X is metrizable and H is a dually embedded subgroup which is also either discrete or bounded torsion. We also give some general principles and point out some errors we have found in the existing literature on this problem. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：15

共 36 条

[1]

Armacost DavidL., 1981, STRUCTURE LOCALLY CO, V68

[2]

Auenhofer L., 1999, THESIS, V384

[3] "Varopoulos paradigm": Mackey property versus metrizability in topological groups [J].