Part of a continuing effort to fight the idea of "Dark Ages" by extending the Renaissance back further and further rather than just pointing out that the Dark Ages were a flawed and propagandistic concept to begin with? (See also: Carolingian Renaissance of the 9th century)
It depends on where you were how much of an effect thee was. After all, the Roman empire lasted until 1453 in Constantinople.
And, I am getting rather annoyed pointing out to people, till 1461 in Trebizond.
You forget Mistra/The Roman Empire still lasts untill today in Moscow!
No -- Mystras fell to the Ottomans in 1460, a full year before Trebizond did. And Moscow is the center of something even more crazy/bizarre than Byzantium.
Mistra/Mystras is more authentically Byzantine, though, actually having a direct link to the last Emperors and not being separated from the Empire untill 1453, whereas Trebizond didn't necessarily recognize the legitimacy of the Emperors in Nicaea and later Constantinople, and as such can only be counted as Roman if we count the Western Empire as well.