[tsimionescu]

Well, I think we could define it by what the people living there considered themselves to be. And generally, from what I know (but I'm not well read on this subject, so I'm happy to be corrected), the inhabitants of the area would have called themselves Romans, at least by the time the city came to be known as Constantinople.

Also, the culture of Athens or Sparta or Crete or any of the other places that would have called themselves, or at least accepted the term, Greeks (well, Hellenes) was quite different from the culture of Constantinople, at least, again, by the time the city came to be known by that name.