1. Give an example that int(A) = int(B) = , but int(A B) is the whole space. 2. (X, d), where d is discrete. Which subsets of X are compact? Explain why. 3. Is every point of every open set A R d an accumulation point of A? Answer the same question for closed sets in R d . 4. Show using the definition of connectedness that the set N is disconnected. 5. Show using the definition of total disconnectedness that the set Q is totally disconnected