3
votes
1answer
312 views

Action on a compact group

If $G$ is an infinite compact group, how many orbits can $G$ have under the group action of its continuous automorphisms ?
19
votes
0answers
848 views

Do all possible trees arise as orbit trees of some permutation groups?

I.Motivation from descriptive set theory (Contains some quotes from Maciej Malicki's paper.) The classical theorem of Birkhoff-Kakutani implies that every metrizable topological group G admits a ...