Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)

Abstract

The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a new example of a quotient map such that q x q fails to be a quotient map. This also settles in the negative the question of whether the fundamental group (with the quotient topology) of a compact metric space is always a topological group with the standard operations.

5 pages. A modified introduction and bibilography

References in corpus (2)

• Discreteness and Homogeneity of the Topological Fundamental Group
• The Topological Fundamental Group and Hoop Earring Spaces

Cited by in corpus (2)

• The topological fundamental group and free topological groups
• Epitopological and pseudotopological fundamental group functors