Prove that:

Let E be a subset of R^d and x an element of R^d. Then:

c) x ∈ ∂E if and only if everyneighborhoodof x contains points of E and points of the complement of E.

(parts a and b of this theorem state: (a) x ∈ int(E) if and only if there is a neighborhood of x that is contained in E; (b) x ∈ E if and only if every neighborhood of x contains a point of E ... I've proven parts a and b though)