What is the mean of bijective is an open condition ? And why the Lie algebra of $Gl(V)$ can be identified with $gl(V)$ ?
Asked
Active
Viewed 171 times
0
-
It's an open condition because an linear endomorphism $T$ of a $n$-dimensional vector space is bijective if and only if $\det T\ne 0$. – Oct 20 '16 at 18:28
-
@G.Sassatelli I know endomorphism is bijective iff $\det T\ne 0$. But I don't know the mean of open condition. What is open condition ? – Enhao Lan Oct 21 '16 at 01:35
-
A condition is open if the set of the elements which satisfy it is open. – Oct 21 '16 at 03:55