True, but the massive cultural shift between the old Romans and the Byzantines does make it easier to speak about two different entities with a shared development. Otherwise you could call Greece a Roman legacy since they saw Constantinopel as their obvious capital during their independence war. The Byzantine empire did end up as a Greek empire quite quickly.
Of course, you also have the 3 self-proclaimed followers of the new roman empire. The Holy Roman Empire, tsarist (ceasarist) Russia and of course the Ottomans themselves.
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