1. Prove: If x is an accumulation point of the set S, then every neighborhood of x contains infinitely many points of S. 2. (a) Prove: bd S = (cl S ) ∩ [cl ( \S )]. (b) Prove: bd S is a closed set. 3....

1. Prove: If x is an accumulation point of the set S, then every neighborhood of x contains infinitely many points of S.

2. (a) Prove: bd S = (cl S ) ∩ [cl (\S )].

(b) Prove: bd S is a closed set.

3. Prove: S ′ is a closed set

4. Suppose S is a nonempty bounded set and let m = sup S. Prove or give a counterexample: m is a boundary point of S.