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Hello everyone
How to show that the special linear group $SL(n,$R$)$ is a closed set of the general linear group $GL(n,$R$)$
I try to show its compliment is an open set by taking every elements in it has an open neighborhood.
However, I do not know how to define the open neighborhood in this case.
Hope someone can help me out.
Thanks.
Note: special linear group means all element has determinant 1
General linear group means the determinant not equal to $0$
How to show that the special linear group $SL(n,$R$)$ is a closed set of the general linear group $GL(n,$R$)$
I try to show its compliment is an open set by taking every elements in it has an open neighborhood.
However, I do not know how to define the open neighborhood in this case.
Hope someone can help me out.
Thanks.
Note: special linear group means all element has determinant 1
General linear group means the determinant not equal to $0$