Concepts of 'Empire' and dominion in Byzantium

As the inheritor of the Roman Empire, I wondered, how did Byzantium conceptualize itself in regards to the world around it? For instance, the Roman Empire saw itself as a worldwide ruler and this propaganda was still alive even as the empire was breaking apart. The new barbarian kingdoms taking over were seen something along the lines of representatives. This was something that existed even in the reign of Justinian.

Another one of its marks was the failure to recognize borders. The Romans never considered their present holdings to be permanent in propaganda and never demarcations were always seen as temporary.

But how did the post-Heraclian Byzantium see itself? How did it view its borders and its size? Did it see it in terms of faith(extent of Orthodox Christianity)? Inheritance from Rome? What was its propaganda? What about in relations to the conquered land in the east and the position of the various kingdoms in the west?

The Empire saw itself as the Roman Empire and its subjects as Romans. The Imperial office was a direct line of sucessors down to augustus. In theory it saw itself as rightful owner of all former Imperial lands and only the ability of Charlemagne forced a reluctant acceptance of a in their eyes subordinate Western Emperor. This attitude persisted and fierce fighting ended Imperial ambitions in Italy. The Empire acknowledged its position through the Heraclian reforms. However, while it acknowledged its new set of realities it also retained its ideology as the all powerful world encompassing bastion of Christianity.