English

The Hawaiian earring group is topologically incomplete

General Topology 2007-05-23 v2 Geometric Topology

Abstract

The premier exhibition of the following phenomenon: The fundamental group of any Peano continuum constructed in similar fashion to the Hawaiian earring admits two natural distinct topological group structures. However despite being uncountable and regular, neither group is a Baire space and hence neither group admits a compatible complete metric.

Cite

@article{arxiv.math/0502148,
  title  = {The Hawaiian earring group is topologically incomplete},
  author = {Paul Fabel},
  journal= {arXiv preprint arXiv:math/0502148},
  year   = {2007}
}

Comments

Introduction and abstract rewritten. 9 pages

R2 v1 2026-07-22T17:15:21.493Z