In that Book I come across following theorem.
Notation 
Author mentioned that by standard argument of compact we can extract sequnce such that $A_{t_{k-1}^{-1}A_{t_k}}\in V$.
I do not understand this standard argument .
I would be really thankful If someone help me out
Any Help will be appreciated
Hint: The operation $\varphi:G\times G\to G,\ (A,B)\mapsto A^{-1}B$ is continuous, hence so is $[0,1]\times[0,1]\to G,\ (t, s) \mapsto A(t)^{-1}A(s)$.
Then the preimage of $V$ is open.
(You can also rely on a metric, if you wish, given by matrix norm.)