Hagia Sofia-The jewel of the Byzantine Empire

 Its been much argued when the Roman empire became the Byzantine empire, the Oxford history of Byzantium suggests two periods.

 The 4th century most probably 395 when the Roman empire was last ruled by a single Emperor.

 OR

 Between 575 and 650, applying to not long after Justinian the greats death to just after Heraclius' death.

 Its really a matter of opinion because its impossible to pinpoint when Rome became Byzantium, however i'll make this compromise, Hagia Sophia was built by a Roman Emperor ruling over an ever increasing Greek empire, so is a combination of both civilisations.

 Yes the empire was divided between, Constantine who got Britannia Gaul and Hispania, Constans who got Italy Africa and the Balkans/Danube and Constantius who got Asia Minor, Syria and Egypt etc. It didnt last long though I think within 2 years, Constantine attempted to seize Constans' territory but was defeated and Constans was later killed by a usurper, leaving Constantius to decide on a western Emperor.

 The point when the Roman empire ceased being Roman is widely open to debate.