Final answer:
The historically accurate sequence of events related to the United States' interests in China's market is the acquisition of colonial territory in Asia, ensuring access to Chinese markets through the 'Open Door' policy, and preventing European nations from monopolizing those markets.
Step-by-step explanation:
The question pertains to the historical sequence of events that were important to the United States in their dealings with China at the turn of the century, primarily concerning the 'Open Door' policy and trade relations. To accurately respond to the student's request for arranging the events, they seem to draw reference to the following historical actions:
- The United States acquired colonial territory in Asia with the acquisition of the Philippines after the Spanish-American War, which later served as a gateway to China.
- John Hay's initiation of the 'Open Door notes' ensured that the U.S. would have access to Chinese markets by advocating for equal trading rights within China's 'spheres of influence'.
- This arrangement effectively prevented European nations from locking the United States out of Chinese markets.
- There was no event where China was allowed to own territory in the United States, this may be a confusion or an error and should not be part of the sequence.
Therefore, the correct order based on significance to the United States would be: 3, 2, 4, ignoring the first option as it is not historically accurate.