Orthogonal matrices are compact

[blaster]

How can you prove that the set of orthogonal matrices are compact? I know why they are bounded but do not know why they are closed.

[HallsofIvy]

What is the topology?


(By the way- closed and bounded does not necessarily imply compact.)

[mathwonk]

how about defining them by an equation?

and of course closed and bounded does imply compact in a euclidean space such as matrix space. as hurkyl knows very well - he is just trying to scare you.

(in a general metric space you need "complete and totally bounded")