Exercise 1, § 3

Let $A, B$ be two subsets of a topological space $X$ such that $A \supset B$. Show that:

a) The interior of $B$ with respect to $X$ is contained in the interior of $B$ with respect to the subspace $A$ of $X$. Give an example where these two sets are distinct.

b) The frontier of $B$ with respect to $A$ is contained in the intersection of $A$ with the frontier of $B$ with respect to $X$. Give an example where these two sets are distinct.