How were lands that were once part of the Byzantine Empire added to the Islamic world?
The Byzantine Empire, also known as the Eastern Roman Empire
No. The Mughal Empire controlled lands that are now part of Afghanistan, Pakistan, Bangladesh, in addition to India.
All of the western lands of the old empire became part of the Byzantine Empire.
Every country bordering the Mediterranean Sea was once part of the Roman Empire. The empire included the complete Mediterranean coastline.
It was the western part of the Roman Empire which collapsed. There are many reasons for this. The most important factor were the invasions of this part of the empire by Germanic peoples who took over all of its lands, expert for Italy. Eventually Italy was also taken over by Germanic peoples. The eastern part of the Roman Empire was not affected by these invasions and continued to exist for another 1,000 years.
All of the western lands of the old empire became part of the Byzantine Empire.
The lands of modern day Turkey were apart of the Byzantine Empire for the most part.
Guatemala was part of the original lands of the Maya who, contrary to popular perceptions, did not form an empire. The expanded their territory, but this was through population increase and migration, rather than empire building. Archaeologists use the term Maya civilisation, not empire.
What fell was neither the city of Rome nor the whole empire. It was the western part or the empire which fell. The eastern part continued to exist for another 1,000 years. The fall of the west was precipitated by the invasions by the Germanic peoples which took over most of the lands in the west.
The Greek eastern part of the Roman empire is known as the Byzantine, or Byzantine Empire.
During the medieval period, the empire called the Roman Empire was centered in Greece and covered only the eastern Mediterranean. It is the empire that we now call the Byzantine empire, to distinguish it from the ancient Roman Empire that was centered on Rome and Italy and came to encompass the entire Mediterranean, as well as lands well beyond.