[Destro]

Are you ignorant on purpose?

From the article:

In the provinces close to Constantinople, where the Greek language predominated over the Latin of Old Rome, the idea of Roman citizenship and identity appealed to a broad segment of the population. Greek speaking citizens were proud to be Romans: in Latin, "Romani," or, in Greek, "Romaioi." The word "Romaioi" became descriptive of the Greek speaking population of the Empire. The old ethnic name applied to Greeks, "Hellene",fell into disuse.

[Tuco Ramirez]

The areas outside the vicinity of Constantinople were held by Turks.

I'll guess you're either Greek (by ethnicity) or Orthodox (by faith); in any case, if Byzantium was such a bulwark for the Roman Empire, why couldn't they save Rome (as good Romans would). Also, why did they have competing emperors in the West and East?

When Muslims invaded Spain, there was no "Crusades" from the East to help push them back across the Straits. The East made various deals with Islam to prevent an earlier (an inevitable) collapse, while the West fought a death struggle against them (Charles Martel in France, the later "Reconquista" in Spain, etc.).