Many people falsely assume that the Roman Empire was a European Empire because the city of Rome is in Europe.  But these people forget that the former Roman Empire spanned three continents; Africa, Asia (the Middle East), and Europe.  The former Roman Empire was not a European Empire, but it was a Mediterranean Empire, centered around the Mediterranean.
     According to The New Encyclopedia Britannica (15th ed., 1995), The former Roman Empire had two legs:  the Roman part and the Byzantine part.  The Roman, or western side, covered parts of southern Europe and parts of North Africa.  The Byzantine, or eastern side, covered parts of southern Europe, the Middle East, and parts of North Africa.

     The Encyclopedia Britannica begins its article on "The History of the Byzantine Empire" as follows:
  

 The western part of the Empire was partially managed from the city of Rome, but in the year 324 the emperor Constantine moved the capital from the city of Rome to the eastern city of Constantinople.  The fall of the city of Rome in the year 476 was not the end of the Roman Empire because that was not the capital city!  The capital of the Empire was Constantinople, and it continued to thrive.  The Byzantine side continued for another thousand years after the fall of the city of Rome!  Later, when the Ottoman Turks conquered Constantinople, the city's name was changed to Istanbul.
     From all of this we can conclude that the former Roman Empire was a Mediterranean Empire composed of North African, Middle Eastern, and southern European regions.  It was called the Byzantine Empire.  The capital city of the Empire was not the city of Rome, as most people assume, but was Istanbul.