The topological Hawaiian earring group does not embed in the inverse limit of free groups

被引：6

作者：

Fabel, Paul ^{[1
]}

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2005年 / 5卷

关键词：

topological fundamental group; inverse limit space; Hawaiian earring;

D O I：

10.2140/agt.2005.5.1585

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Endowed with natural topologies, the fundamental group of the Hawaiian earring continuously injects into the inverse limit of free groups. This note shows the injection fails to have a continuous inverse. Such a phenomenon was unexpected and appears to contradict results of another author.

引用

页码：1585 / 1587

页数：3

共 13 条

[1] A retraction theorem for topological fundamental groups with application to the Hawaiian earring
Fabel, Paul
[J]. TOPOLOGY AND ITS APPLICATIONS, 2007, 154 (03) : 722 - 724
[2] Free subgroups of the fundamental group of the Hawaiian earring
Eda, K
[J]. JOURNAL OF ALGEBRA, 1999, 219 (02) : 598 - 605
[3] INVERSE LIMIT OF FREE NILPOTENT GROUPS
BAUMSLAG, G
STAMMBACH, U
[J]. COMMENTARII MATHEMATICI HELVETICI, 1977, 52 (02) : 219 - 233
[4] Generating the inverse limit of free groups
Conner, Gregory R.
Herfort, Wolfgang
Kent, Curtis A.
Pavesic, Petar
[J]. JOURNAL OF ALGEBRA, 2021, 578 : 371 - 401
[5] The topological fundamental group and free topological groups
Brazas, Jeremy
[J]. TOPOLOGY AND ITS APPLICATIONS, 2011, 158 (06) : 779 - 802
[6] On free topological groups with the inductive limit topologies
Sipacheva, OV
[J]. PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS: TENTH SUMMER CONFERENCE AT AMSTERDAM, 1996, 788 : 188 - 196
[7] Group laws and free subgroups in topological groups
Abért, M
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2005, 37 : 525 - 534
[8] Free topological groups over (semi) group actions
Levy, MM
[J]. PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS: TENTH SUMMER CONFERENCE AT AMSTERDAM, 1996, 788 : 164 - 169
[9] The big fundamental group, big Hawaiian earrings, and the big free groups
Cannon, JW
Conner, GR
[J]. TOPOLOGY AND ITS APPLICATIONS, 2000, 106 (03) : 273 - 291
[10] VARIETY OF TOPOLOGICAL GROUPS GENERATED BY FREE TOPOLOGICAL GROUP ON [0,1]
MORRIS, SA
[J]. COLLOQUIUM MATHEMATICUM, 1976, 36 (02) : 205 - 213

← 1 2 →