It was a direct continuation of the roman empire wasnt it. The empire disintegrated in the west, but the part that was in the east survived - with its capital in Constantinople. There was no break, and the greeks didnt go and conquer the eastern roman empire to make it their own. The culture simply morphed over time. But then the culture of Rome at the end was nothing like the culture of the city state that fought the carthaginians and then started dreaming of empire. Cultures constantly evolve. Britain now is nothing like the island conquered by the romans, but its still Britain. England now isnt even the same as the country ruled by Victoria, and that was only 100 years ago!
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