Topological group

  • Thread starter tomboi03
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Let H be a subspace of G. Show that if H is also a subgroup of G, then both H and[tex]\bar{H}[/tex] are topological groups.

So, this is what i've got...

if H is a subgroup of G then H [tex]\subset[/tex] G.
Since H is a subspace of G then H is an open subset.

But, i don't even know if that's right.
How do i do this?

Thanks!
 
Clearly H is a group and it's a topological space. It need not be an open set on the topology on G (if it's a subspace in the sense I think you mean - a subset with the subspace topology).

What you need to show is that the restrictions of the multiplication and inverse maps to H are still continuous.
The [tex]\overline{H}[/tex] is more tricky. You need to show that it is closed under the operations too.

Let me know if this helps?
 

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