Byzantium is a term used by modern historians to refer to the later Roman Empire.
In its own time, the Empire ruled from Constantinople (or "New Rome" as some people call it, although this was a laudatory expression that was never an official title) was considered simply as "the Roman Empire."
The fall of Constantinople led competing factions to lay claim to being the inheritors of the Imperial mantle.
Russian claims to Byzantine heritage clashed with those of the Ottoman Empire's own claim.
In Mehmed's view, he was the successor to the Roman Emperor, declaring himself Kayser-i Rum, literally "Caesar of Rome", that is, of the Roman Empire, though he was remembered as "the Conqueror".
 He founded a political system that survived until 1922 with the establishment of the Republic of Turkey.

Stefan Dušan, Tsar of Serbia, and Ivan Alexander, Tsar of Bulgaria, both made similar claims, regarding themselves as legitimate heirs to the Roman Empire.
Other potential claimants, such as the Republic of Venice and the Holy Roman Empire have disintegrated into history.
Byzantium is a term used by modern historians to refer to the later Roman Empire. In its own time, the Empire ruled from Constantinople (or "New Rome" as some people call it, although this was a laudatory expression that was never an official title) was considered simply as "the Roman Empire." The fall of Constantinople led competing factions to lay claim to being the inheritors of the Imperial mantle. Russian claims to Byzantine heritage clashed with those of the Ottoman Empire's own claim. In Mehmed's view, he was the successor to the Roman Emperor, declaring himself Kayser-i Rum, literally "Caesar of Rome", that is, of the Roman Empire, though he was remembered as "the Conqueror".  He founded a political system that survived until 1922 with the establishment of the Republic of Turkey.
Stefan Dušan, Tsar of Serbia, and Ivan Alexander, Tsar of Bulgaria, both made similar claims, regarding themselves as legitimate heirs to the Roman Empire. Other potential claimants, such as the Republic of Venice and the Holy Roman Empire have disintegrated into history.
Fall of Constantinople