A retraction theorem for topological fundamental groups with application to the Hawaiian earring

2005/02/10 by Paul Fabel, Fabel, Paul
Mathematics · #54H11 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GN #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0502218

4 pages

arxiv created 2005/02/10 · openalex publication_date 2005/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.

Citations

• The Hawaiian earring group is topologically incomplete
• The fundamental group of the harmonic archipelago

Related

• The Hawaiian earring group and metrizability
• The Hawaiian earring group is topologically incomplete
• Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)
• The Topological Fundamental Group and Hoop Earring Spaces
• Every group retraction can be realized as a topological retraction