1. Prove: If x is an isolated point of a set S, then x ∈ bd S. 2. If A is open and B is closed, prove that A\B is open and B\A is closed 3. Prove: For each x ∈  and ε > 0, N*(x ; ε) is an open set. 4....

1. Prove: If x is an isolated point of a set S, then x ∈ bd S.

2. If A is open and B is closed, prove that A\B is open and B\A is closed

3. Prove: For each x ∈
 and ε > 0, N*(x ; ε) is an open set.

4. Prove: (cl S )\(int S ) = bd S.

5. Let S be a bounded infinite set and let x = sup S. Prove: If x ∉ S, then x ∈ S ′.