Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Normal subgroup; topological group

  1. Mar 24, 2009 #1
    The integers Z are a normal subgroup of (R,+). The quotient R/Z is a familiar topological group; what is it?

    okay... i attempted this problem....
    and I don't know if i did it right... but can you guys check it?


    R/Z is a familiar topological group
    and Z are a normal subgroup of (R,+)
    then the quotient R/Z is also a topological group with the quotient topology.
    The R/Z is Hausdorff iff Z is a closed subset of (R,+) which in this case is true.
    Therefore, R/Z is a quotient topology.

    sorry if there are a lot of things that didn't make sense in that proof but i tried.... hahaha
  2. jcsd
  3. Mar 24, 2009 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    That's not what it's after. It's asking you to identify it (name it, if you will) as a topological group. What topological groups do you know?

    You're taking the real line and identifying x and y if x-y is what? I.e. x and y differ by what? What is a good choice for a set of equivalence classes of cosets?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook