Volume 5, issue 4 (2005)

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

Paul Fabel

Algebraic & Geometric Topology 5 (2005) 1585–1587

arXiv: math.GN/0501482

Abstract

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.

Keywords
topological fundamental group, inverse limit space, Hawaiian earring
Mathematical Subject Classification 2000
Primary: 57M05, 14F35
Secondary: 54H10, 22A10
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Publication
Received: 15 2005
Revised: 22 October 2005
Accepted: 24 October 2005
Published: 24 November 2005
Authors
Paul Fabel
Drawer MA
Department of Mathematics and Statistics
Mississippi State University
Mississippi State
MS 39762
USA