Countably compact group topologies on arbitrarily large free Abelian groups

被引：0

作者：

Bellini, Matheus K. ^{[2
]}

Hart, Klaas Pieter ^{[1
]}

Rodrigues, Vinicius O. ^{[3
,4
]}

Tomita, Artur H. ^{[2
]}

机构：

[1] Delft Univ Technol, Fac EEMCS, Postbus 5031, NL-2600 GA Delft, Netherlands

[2] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

[3] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

[4] York Univ, Dept Math & Stat, Keele St 4700, Toronto, ON M3J 1P3, Canada

来源：

TOPOLOGY AND ITS APPLICATIONS | 2023年 / 333卷

基金：

瑞典研究理事会; 巴西圣保罗研究基金会; 加拿大自然科学与工程研究理事会;

关键词：

Topological group; Countable compactness; Selective ultrafilter; Free Abelian group; Wallace's problem; CARDINALITY C; POWERS; QUESTION; WEIGHT; SQUARE;

D O I：

10.1016/j.topol.2023.108538

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if there are c incomparable selective ultrafilters then, for every infinite cardinal kappa such that kappa omega = kappa, there exists a group topology on the free Abelian group of cardinality kappa without nontrivial convergent sequences and such that every finite power is countably compact. In particular, there are arbitrarily large countably compact groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：23

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