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Topological group

  1. Mar 24, 2009 #1
    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?

  2. jcsd
  3. Mar 27, 2009 #2
    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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