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Homeomorphism calculation help

  1. Apr 18, 2008 #1
    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 18, 2008 #2


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    If you think of A as a matrix, how about just replacing the first row with the negative of itself? Isn't that an explicit homeomorphism?
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