- Thread starter
- #1

- Thread starter smile
- Start date

- Thread starter
- #1

- Moderator
- #2

- Feb 7, 2012

- 2,702

What have you tried so far? I suggest you stick to the case $n=2$ and write down explicitly what it is that you need to prove the result in that case.Is anyone can help me to show The determinant function: det: M(n*n)-->R is continuous. and Justify it for the case n = 2.

where M(n*n) is a n by n matrix

Thanks

- Thread starter
- #3

Hello, i think we can take an open set in $R$ and show its pre-image is open, right? However, I do not know how to find the pre-image in this case.What have you tried so far? I suggest you stick to the case $n=2$ and write down explicitly what it is that you need to prove the result in that case.

Thanks

- Moderator
- #4

- Feb 7, 2012

- 2,702

Hint: you know that sums and products of continuous functions are continuous. So all you really need to do here is to explain why the coordinate functions, such as $(w,x,y,z)\mapsto w$, are continuous.

- Jan 29, 2012

- 661

- Thread starter
- #6

Thanks for your help, I think I have figured out this problem.

Hint: you know that sums and products of continuous functions are continuous. So all you really need to do here is to explain why the coordinate functions, such as $(w,x,y,z)\mapsto w$, are continuous.

- - - Updated - - -

Thank you.Opalg, is based on the fact that all finite dimensional vector with the same dimension, are homeomorphic.