Could anybody give me a hand to prove the following question that I have just seen on the book? I really appreciate your help!
Let $X$, $d(x, y)$ be a metric space and $A ⊂ X$, $B ⊂ X$. Prove the following formulas:
(a) $∂(A ∪ B) ⊂ ∂A ∪ ∂B$.
(b) $int(A ∪ B) ⊃ int(A) ∪ int(B)$.
(c) Show by examples that in general there is no equality in (a) and (b).