topolog 16. Let (X,9) be a topological space and let ACX. Prove the following: ood of such the int Desc The point and c (a) The boundary A is a closed set. (b) A is both open and closed if and only if OA = 0. (c) A is open if and only if OAC A'./ 17. Let (X,) be a topological space and let AC X. A point x = X is said to be an exterior point of A if there exists a neighborhood N of z such that NOA=0. The collection of all exterior points of A is called the exterior of A and is denoted by ext(A). Show that ext(A) = (A') = (A)'. 18. Let (X, 9) be a topological space and let A and B be subsets of X. (a) Prove that (An B)° = A°n B°. (b) Give an example to show that (AUB) = A° UB° is not necessarily true. 19. Give an example of a topological space (X, 9), a subspace (Y), and suboots 4 n shoti