1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Toplogical group

  1. Jul 2, 2011 #1
    1. The problem statement, all variables and given/known data
    Let H be a subspace of G. show that if H is also a subgroup of G then the closure of H is a topological group
    G is a topological group

    2. Relevant equations

    3. The attempt at a solution
    let closure of H is a subspace of G then the map of the operation of G restricted to cl(H) is continuous
    I have the A2 axiom satisfied for cl(H) but I cant prove the the A1 + A3 +A4
  2. jcsd
  3. Jul 2, 2011 #2
    A1-4 doesn't tell us anything, please write them down. It is hard to help you if we don't know which definition of a topological group you use.
  4. Jul 2, 2011 #3
    A1: for all x y in G xRy is in G
    A2 : for all x,y ,z in G xR(yRz) = (xRy)Rz
    A3 : for all x in G there exists a 0 in G such that xR0=0Rx=x
    A4: xRx^-1 = 0 = x^-1 R x
  5. Jul 2, 2011 #4
    Hi NeroKid! :smile:

    You know that

    [tex]f:G\times G\rightarrow G:(x,y)\rightarrow x*y[/tex]

    is continuous. And since H is a subgroup, you know that

    [tex]f(H\times H)\subseteq H[/tex]

    Now, what can you say about

    [tex]f(cl(H)\times cl(H))[/tex]
  6. Jul 2, 2011 #5
    tks i get it know ;))
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Toplogical group
Are these homomorphisms?