And I can’t decide where to put it in either article.

Maybe we should splitt off an entry *p-adic integer* from *p-adic number* anyway. The non almost-connectedness would naturally be discussed there and then we could point to that from the other two entries.

The example if $p$-adic integers isn’t in either article. And I can’t decide where to put it in either article.

]]>This example is mentioned already at *maximal compact subgroup*. But it would be nice if somebody found the time to add it also to *almost connected topological group*, highlighting the point just discussed.

(I guess I could do it later. But I won’t protest if somebody does it before me ;-)

]]>Thanks.

]]>Zoran, as an example, consider the $p$-adic integers under addition. This is totally disconnected, so the connected component $G_0$ is just the identity element. Therefore $G/G_0 \cong G$, and $G$ is compact Hausdorff, so this is an example.

]]>It says the “quotient topological space $G/G_0$” and it means the quotient topological group. I know, you wanted to say the underlying space of the quotient topological group, but if one talks about quotient topological space then this means that only $G_0$ is contracted to a point, while the rest stays the same. In other words, the notation $G/G_0$ in topological category is much bigger than the underlying space of $G/G_0$ in the category of topological groups. The quotient in the category of topological spaces is different than the underlying topological space of a quotient in the category of topological groups. I corrected the statement.

But a real question is if the entry assumes Hausdorfness. I wonder how one can have compact quotient of topological groups by a connected component if not finite, as if something is an accumulation point, by the homogeneity, everything would be an accumulation point. Example ?

]]>just for completeness, I have created an entry *almost connected topological group*.