[VadeRetro]

Actually Rome did not fall until the 1400s when the city of Byzantium and it's environs were seized by the Turks (who were, by that time, quite civilized themselves, or things would have been much, much worse).

The Constantinople that fell to the Turks in 1453 had indeed been the capital of Constantine, but it had already fallen once in the Fourth Crusade. There was no Byzantine ("Roman") Empire for almost 60 years, 1204 to 1261, the duration of something called the Latin Kingdom of Constantinople. Continuity was lost there. 1204 should probably be marked as the disappearance of the last remaining real shreds of the Roman Empire.

Yes, that nation still in 1453 called itself the Roman Empire. Nevertheless it was a small, uniformly Greek-speaking kingdom, no empire at all. It had lost the last shreds of empire centuries earlier. Nor was it the last kingdom to style itself the Roman Empire. Attempted revivals include the Holy Roman Empire and Napoleon crowning himself as Roman Emperor as late as 1800.

[Cronos]

the Turks (who were, by that time, quite civilized themselves, or things would have been much, much worse)
Quite correct, the Turks/Mongols were civilised quite a bit by that time (100 years after the butcher Timur e Lang)

[Cronos]

Nor was it the last kingdom to style itself the Roman Empire. Attempted revivals include the Holy Roman Empire and Napoleon crowning himself as Roman Emperor as late as 1800.

The Dukes of Moscow called themselves Caesar or Tsar and styled Moscow as the Third Rome. The German Kings called themselves Kaiser, Caesar.