For a topological space X, the fundamental group can be topologized as a quotient of the path space with the compact-open topology. For one-dimensional or planar Peano continua, the fundamental group with this topology is a topological group if and only if it is semilocally simply connected. In particular, we demonstrate that the group operation is not continuous in this setting.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-10720 |
| Date | 01 August 2022 |
| Creators | Steadman, Eric |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | https://lib.byu.edu/about/copyright/ |
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