Hello! I need to show that Lorentz Group is non compact, but has 4 connected components. The way I was thinking to do it is to write the relation between the elements of the 4x4 matrices and based on that, associated it with a known topological space, based on the determinant and the value of the (0,0). However if I am not wrong it would be a 16 dimensional space, so I kinda got scared. I assume there is an easier way. Can someone help me a bit, give send me a link with the proof? Thank you!