Topology practice

cl(A ∪ B) = cl(A) ∪ cl(B) for any two subsets

cl(A ∩ B) = cl(A) ∩ cl(B) for any two subsets

int(A ∩ B) = int(A) ∩ int(B)

The box topology on $\mathbb{R}^\mathbb{N}$ is finer than the product topology