Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter

被引：7

作者：

Boero, A. C. ^{[1
]}

Pereira, I. C. ^{[2
]}

Tomita, A. H. ^{[3
]}

机构：

[1] Univ Fed Abc, CMCC, Rua Abolicao S-N, BR-09210180 Santo Andre, SP, Brazil

[2] Univ Fed Para, Inst Ciencias Exatas & Nat, Rua Augusto Correa 01, BR-66075110 Belem, Para, Brazil

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

来源：

ACTA MATHEMATICA HUNGARICA | 2019年 / 159卷 / 02期

基金：

巴西圣保罗研究基金会; 瑞典研究理事会;

关键词：

topological group; countable compactness; selective ultrafilter; free Abelian group; Wallace's problem; QUESTION; POWERS;

D O I：

10.1007/s10474-019-00991-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a consequence, we show that the existence of a selective ultrafilter implies the existence of a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topologicalgroup).

引用

页码：414 / 428

页数：15

共 44 条

[1] Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter
A. C. Boero
I. C. Pereira
A. H. Tomita
[J]. Acta Mathematica Hungarica, 2019, 159 : 414 - 428
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[9] Countably compact group topologies on non-torsion Abelian groups of size continuum with non-trivial convergent sequences
Bellini, Matheus Koveroff
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[J]. TOPOLOGY AND ITS APPLICATIONS, 2019, 267
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