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Questions about the branch of algebra that deals with groups.

0 votes
0 answers
343 views

Isometry group of a complete separable metric space is Polish?

Let $(X,d)$ be a complete separable metric space, and endow $Iso(X,d)$ with the pointwise convergence topology. I've seen a few sources say this is clearly a Polish group, but why is this this the c …
pseudocydonia's user avatar
16 votes
3 answers
1k views

What are some interesting examples of non-classical dynamical systems? (Group action other t...

By classical dynamical system, I mean a measure space together with a measurable action of the integers or the reals. Of course, this action is often interpreted as evolution with respect to discrete …