The Hawaiian earring group is topologically incomplete

Details The Hawaiian earring group is topologically incomplete The Hawaiian earring group is topologically incomplete

2005-02-07

arxiv.org/abs/math/0502148v2

Mathematics

General Topology

Introduction and abstract rewritten. 9 pages

Scientific paper

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.

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