Please see the attached file for full problem description.
Let A and B be closed subset of Rn with A ∩ B = Ø.
a. Prove that ∀u ∈ A, ∃_ > 0 such that N_ (u) ∩ B = Ø
b. Prove that there is an open set OA satisfying OA ⊃ A and OA ∩ B = Ø
c. Prove or find a counterexample: There are open sets OA and OB satisfying OA ⊃ A,
OB ⊃ B = B and OA ∩ OB = Ø
This is three proofs about a closed subset of Rn, including two about open sets.