How roman empire lived on , even though it died 476ad

186734 Roman Empire declined and fell in 476 AD according to all Western historical evidences, even though the relevance of this is questioned by many modern historians, who argued that Eastern Roman Empire continued to flourish till 1453, the year of Fall of Constantinople. So Fall of Rome was not the end of Roman Empire and 476AD is also known to be the beginning of the medieval age.
There had been two emperors, one in the East, usually in Constantinople and the other in the West. Odoacer, who became the first ‘ barbarian’ king to rule the Western Empire, deposed the Emperor Romulus, who lived in Italy’s Ravenna in a bloodless coup in 476ad; but Emperor Zeno continued to live and rule in Constantinople, whose authority was acknowledged by Odoacer himself.
Roman power continued in the East, under rulers of Constantinople and a ‘ fall’ was not particularly noticed. East Roman Emperors considered themselves as the real Roman Emperors, right heirs to Augustus. Byzantine was part of Roman history and 476ad was more of a Western point of view it was the continuation of Roman empire and the fall of Western empire was simply ignored and the division of the two was not particularly glorified because there was no such formal division and they remain. Even the promulgated rules applied to the entire territory, because in spite of two empires, the empire remained one for a very long time. Hence, there was a change in the region and the empire no doubt lost some of its glitz; but there was no fall.
The Byzantine flourished diplomatically with many countries. It became the centre of literature, culture, religion and architecture. Roman Catholic Church continued to exist and it represented the lost empire with very little change while Byzantine survived for another thousand years. In a way it was a glorious period under Justinian like rulers. Religion was becoming more and more prominent; but the emperors retained their authority fully. In latter fifth century, the emperor estranged himself from Roman Pope by declaring himself Monophysite, which was discarded by Justin, an action that gained Pope’s support. Byzantine Christianity was slightly different from the Latin Christianity and culture. They thought ecclesiastical and theological authority vested in the Emperor and not with Pope and his minions. But adoption of strict traditional ways made it an absolutely static religion. The Empire pursued classical and intellectual traditions of education, philosophy, composition, literature, history. Women were well educated like Comnena who wrote the famous biography. Through Byzantine, classic Greek and Roma culture were transmitted into Islam while religion reached Slavics, especially the Russians. It became the most prominent civilisation of the medieval period in spite of harsh legal system and internal and external strife. But there was a cultural enhancement, support and appreciation of art and architecture, no doubt, it got isolated from rest of Europe, but it was a highly active empire, though diminished in size. The promulgation of Corpus Juris Civilis, an unprecedented legal achievement during Justinian period, unparalleled architecture of Santa Sophia and San Vitale decorated with unique mosaic style with the largest ever dome, Hence, 476ad did not spell the death knell of Roman Empire. Politically this empire prevented Islam from spreading into Europe till its fall. Muslims found Byzantine a major road block when they tried to conquer Europe for spreading the religion.