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Topologies Invariant Under A Group Action, Paul Bankston
Topologies Invariant Under A Group Action, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
We study links between faithful group actions on a set and topologies on that set. In one direction, a group action has its invariant topologies (so we may regard members of the action to be homeomorphisms relative to those topologies); in the other direction, a topology has its preserving group actions (i.e., the subgroups of the homeomorphism group of the topology). This two-way passage allows us to discuss topological features of group actions as well as symmetry features of topologies.