I need to prove
i) lim n to infinity sup Sn is an element of SL(Sn)
ii) same thing but replace sup with inf
I know SL(Sn) is the set of all limits of all convergent subsequences of Sn.
Also, lim n to infinity sup Sn can be defined as sup SL(Sn)
So it may be easier to show that Sup SL(Sn) is an element of SL(Sn)