An Empire is the political system where a nation or a group of nations are controlled by a ruler and they occupy a big extension of land. Even when the empire has geographical limits, its influence and power can spread to other countries. A good example is the old saying "All the roads lead to Rome" because Rome was the capital of the Roman Empire, and even when you were far from it, you could be sure the main roads were connected with this city. Likewise, empires have colonies or protectorates in order to expand their territories.
Thus, the right answer is option 4, imperialism.
