Final answer:
Alfred Mahan did not believe the reopening of the American frontier was needed to build an American empire; he emphasized the need for a strong navy, military bases, and a canal through Central America.
Step-by-step explanation:
The question asks which of the following Alfred Mahan did not believe was necessary to build an American empire. According to the information provided, the correct answer is C: the reopening of the American frontier. This answer is based on the understanding of Mahan's beliefs, where he emphasized the importance of a strong navy, military bases around the world, and a canal through Central America for strategic and economic reasons, but not the reopening of the American frontier.