All Questions

Let $G$ be a profinite group and $H$ be an open subgroup. As a continuous $H$-topological space, we have $G=\coprod_{G/H} H$. Does this also hold as condensed sets, i.e. do we have an identification ...

A compact topological group $G$ is called Van der Waerden if each homomorphism $h:G\to K$ to a compact topological group is continuous. By a classical result of Van der Waerden (1933) the groups $SO(...

Let $A\rightarrow B\rightarrow B/A$ be a short exact sequence of topological groups. Is it true that if there exists a continuous function $B/A\rightarrow B$ (of underlying spaces) such that the ...

When I first met the concept of "characters" of topological groups in Pontryagin's book "Topological groups", it was defined as follows: Let $G$ be a topological group. A ...

There are a lot of compact (Hausdorff) groups, whereas every compact field is finite. What about rings? Is there a classification theorem for compact rings? If you take a cofiltered limit of finite ...