What were main changes and continuities, in the eastern mediterranean, between patterns during the roman empire and patterns in the postclassical period?

The eastern Mediterranean was once known as the eastern Roman empire before the actual fall of Rome in the 5th century, but it was later known as the Byzantine empire throughout the rest of the middle ages. It was known as the actual successor the the Roman Empire as oppose to the growing Holy Roman Empire in the German lands. The main changes were 1st its name, it renamed itself as the Byzantine empire. 2nd, was the revision of the Roman laws into the so-called Justinian code. 3rd is the rise of the new type of architecture that differ much from the old Roman, it blended the eastern arab and roman architecture, the best example is the Hagia Sophia. Their Capital Constantinople as opposed to Rome was founded in Christian origin rather than the polytheistic Greco-Roman religion. Their problems were also different in a way that Rome was located in the sea so basically it lacks the problem of naval warfare compared to Constantinople which is always under threat of the growing Islamic sphere. The continuity was found in the field of politics, economy, military and culture, much of the Roman influences are still found in this new empire. The writings of the classics like Plato's and other greek philosophers were developed and maintained unlike in the west where much of it was forgotten. Sciences were preserved and cultivated.