The Hawaiian earring group is topologically incomplete
arXiv:math/0502148
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.
Introduction and abstract rewritten. 9 pages
References in corpus (5)
- The fundamental group of the harmonic archipelago
- Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
- A characterization of spaces with discrete topological fundamental group
- A monomorphism theorem for the inverse limit of nested retracts
- A retraction theorem for topological fundamental groups with application to the Hawaiian earring
Cited by in corpus (4)
- Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
- A characterization of spaces with discrete topological fundamental group
- A monomorphism theorem for the inverse limit of nested retracts
- A retraction theorem for topological fundamental groups with application to the Hawaiian earring