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