Re: Topological groups question

On Wed, 13 Feb 2008, Arturo Magidin wrote:
James <james545@xxxxxxxxx> wrote:

If G is a topological group and H is a subgroup of
index n, then is the
topological closure of H also a subgroup of index

I'm not asking if a subgroup of index n is closed. I'm asking
whether or not the closure of a subgroup of index n is also a
subgroup of index n.

No. [R;Q] is uncountable, [R:cl Q] = 1

If the closure of the subgroup properly contains the subgroup, how
could the index fail to be strictly smaller? After all:

[G:H] = [G:cl(H)][cl(H):H].

.

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