The world of Basileia ton Romaion (Byzantine Empire in Greek), is a world where Byzantium still thrives until today.
The Fourth Crusade never ransacked Constantinople, leaving the Empire alive.
The following emperors carried the legacy of their ancestors and expanded the territory into all of Anatolia and Levant.
The empire ultimately collapses in 1919 in the aftermaths of World War I. The successor state, the Byzantine Republic exists until nowadays.