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

The set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0

  1. Apr 17, 2008 #1
    Could any one help me to prove the following question:
    "How can we show that the set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0}?"
     
  2. jcsd
  3. Apr 17, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Have you tried to write down a homeomorphism?
     
  4. Apr 18, 2008 #3
    Thanks for reply. Yah I mean Homeomorphism. Actually I would ike to know how can we show that the set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0}. I didnt understand how can we explain the properties of Homeomorphism function here. Could you please tell me a little detail. Thanks again.
     
  5. Apr 18, 2008 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    I meant, have you tried to give an explicit homeomorphism between those two sets? It shouldn't be too hard.
     
  6. Apr 20, 2008 #5

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    Rifat ,I hope this is not too obvious of a comment:
    Think of the topology you are using in GL(n;R) , the properties of det (A),and it
    should become clearer.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0
Loading...