How does boxer rebellion relates to open door?

In 1898, US President William McKinley announced his desire for a policy that would allow countries equal access to trade with China. In effect, there'd be an "open door" to Chinese trade, and one country couldn't close the door to another country. President McKinley was concerned the US would be forced out of the Chinese trade by Japan and other European countries, and he wanted a policy that explicitly protected the US's right to continue trading with China.

As a result, in 1899, US Secretary of State John Hay began circulating diplomatic notes among the major world powers (Great Britain, Germany, France, Italy, Japan, and Russia) at the time to get the Open Door Policy formally approved. Because of his work doing this, Hay is often seen as the author of the Open Door Policy.

The creation of the Open Door Policy increased foreign influence in China, which led to a rise in anti-foreign and anti-colonial sentiment in the country. The backlash against foreigners led to widespread killings of missionaries working in China and an increase in nationalist feelings among the Chinese. The Boxer Rebellion was one of the most important events caused by this anti-foreign movement.

The Boxer Rebellion started in 1899, when a Chinese group known as the Society of Righteous and Harmonious Fists (known as "Boxers" to the English) initiated an uprising against foreign influence. The US, Japan, and several European countries fought back and eventually defeated the Boxers in 1901. Even after the rebellion ended, foreign soldiers continued killing and looting in many villages.

The Boxer Rebellion weakened the power of the Chinese ruling dynasty and contributed to the end of Europeans' attempts to colonize China.