Which group or event eventually ended the Byzantium empire​

In the longer term, the rise of Turkish power in Anatolia eventually gave rise to the Ottoman Empire which rapidly conquered the former Byzantine heartland over the course of the 14th and 15th centuries, culminating in the Fall of Constantinople to the army of Sultan Mehmed the Conqueror in 1453.

A. cost too many American lives.

The United States already knew they would win the war way before they attacked Japan. They decided to use an extreme measure as it would, without a doubt, put an end to the war. They thought sacrificing Japan civil people was worth it as long as it meant ending the war as quickly as possible, saving many American lives.