Let X be a topological space, and let A, B, and C be nonempty subsets of X such that A c B c C; that is, A is a proper subset of B, and B is a proper subset of C. Which of the following statements is (are) true?
I. If A and C are connected, then B is connected.
II. If A and C are compact, then B is compact.
III. If A and C are Hausdorff, then B is Hausdorff.
(A)I and II only (B)III only (C)I and III only (D)I, II, and III
D