## New answers tagged topological-groups

1

Like Igor's response, "this is not an answer". It is more of comment that is too long to include as a comment and it also complements Igor's response.
Definition If $G$ is a group acting on $\mathbb{N}$ and $n\in\mathbb{N}$, then $G_n$ denotes the stabilizer of $n$ in $G$. If $X$ is a subset of $\mathbb{N}$, $G_{X}$ denotes the pointwise-stabilizer of $X$.
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3

I am not absolutely sure what is the question.
The answer to the question appearingin in the body is given in a comment by Noam Elkies and the answer to the question given in the title is given by a comment of mine.
Let me answer a third question which is implied and it is less trivial:
which subgroups of $\mathbb{R}^*_+$ appear as images of the modular ...

2

The answer to your questions 1 and 3 is that there is a universal way to do it, but I don't know how this works for infinite linear combinations.
Unfortunately, I only know how to do it in the category of compactly generated topological spaces (or any cartesian closed category of spaces, really). Hence by a topological ring I mean a ring $R$ equipped with a ...

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