Is the Closure of a Subset in l^{1} Compact?

[BobSun]

Homework Statement

Consider the Banach Space $$l^{1}$$. Let S={$$x \in l^{1}|\left\|x\right\|<1$$}. Is S a compact subset of $$l^{1}$$? prove or Disprove.

 

[morphism]

S isn't even closed. A more interesting problem is whether the closure of S is compact, and I suspect this is what you're supposed to work on.