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

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-64.abs.html

References in corpus (2)

• The fundamental group of the harmonic archipelago
• Topological fundamental groups can distinguish spaces with isomorphic homotopy groups

Cited by in corpus (9)

• The fundamental group as a topological group
• Discreteness and Homogeneity of the Topological Fundamental Group
• Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
• The Hawaiian earring group is topologically incomplete
• The Hawaiian earring group and metrizability
• A characterization of spaces with discrete topological fundamental group
• A monomorphism theorem for the inverse limit of nested retracts
• Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)
• On zero dimensional sequential spaces