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

  • Thread starter rifat
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Main Question or Discussion Point

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}?"
 

Answers and Replies

morphism
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Have you tried to write down a homeomorphism?
 
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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.
 
morphism
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I meant, have you tried to give an explicit homeomorphism between those two sets? It shouldn't be too hard.
 
WWGD
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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.
 

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