Why not? Everyone else seems to be considering the Romans and the Byzantines to be a single contiguous entity. Sauce for the goose.
This is totally different for the islamic empires. The invovled massive chamges of the leading elites, internal organisation, sometimed completly know peoples.
Saying the Ottomans were continues with the older empires is ridiculus assertion.
I'm not sure how a state which can trace a direct lineage of law and rulers back to Romulus is "carrying the torch".
Then again, despite being an engineer by trade, I'm a historian specializing in Late Roman Antiquity (specifically, the Eastern Empire from Leo the Isaurian to Alexios I, so I'm probably a little pedantic about it.