Bolzano-Weierstrass theorem holds in any NLS. (Normed Linear Space). Is this statement True?
If it is true how to prove it.
I know how to prove it in $\mathbb R$. I proved it in $\mathbb R$ by using supremum infimum of the set. But in NLS supremum infimum concept do not exist.
Can anyone please help me by giving any hint.