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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Steadman, Eric, "On Continuity of Multiplication in the Fundamental Group" (2022). Theses and Dissertations. 9711.
topological group, fundamental group, semilocally simply connected, Peano, planar, one-dimensional