# Homework Help: Banach Space and Compactness

1. Dec 4, 2008

### BobSun

1. The problem statement, all variables and given/known data
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.

2. Dec 5, 2008

### 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.