Final answer:
Alfred T. Mahan's work on naval power influenced American foreign policy, particularly through the Roosevelt Corollary's emphasis on acting as a regional power and the Open Door Policy's goal of equal trade access in China, all aimed at expanding American influence and commerce.
Step-by-step explanation:
The interconnection between Alfred T. Mahan's 'The Influence of Sea Power Upon History', the Roosevelt Corollary, and the Open Door Policy all relate to the expansion of American influence and commerce in the late 19th and early 20th centuries. Mahan's work emphasized the vital role of naval power in achieving economic and military supremacy.
These ideas influenced Theodore Roosevelt, who as president, applied them in his foreign policy, specifically through the Roosevelt Corollary which was an extension of the Monroe Doctrine stating that the United States would act as an international police power in the Western Hemisphere to prevent European intervention. Additionally, Mahan's emphasis on strategic naval bases and a powerful navy complemented the objectives of the Open Door Policy, which sought equal trading rights for all nations in China and the protection of Chinese territorial integrity against European colonization.
In essence, Mahan's naval strategy provided the blueprint for the United States' approach to international relations and expansion during this period, influencing key policies that asserted American presence and interests abroad.