The Hawaiian earring group and metrizability

Abstract

Endowed with quotient topology inherited from the space of based loops, the fundamental group of the Hawaiian earring fails to be metrizable. The fundamental group of any space which retracts to the Hawaiian earring is also nonmetrizable.

5 pages

References in corpus (2)

• A monomorphism theorem for the inverse limit of nested retracts
• A retraction theorem for topological fundamental groups with application to the Hawaiian earring