Other than modern day arbitrary interpretation, isn't the byzantine empire the roman empire? They were called romans by each other and their neighbors. The roma

Other than modern day arbitrary interpretation, isn't the byzantine empire the roman empire? They were called romans by each other and their neighbors. The roman empire fell when the ottoman turks invaded. Ship of thessius and all. The empire slowly changed in many ways but people considered it rome until the ottomans. When did the british empire end? Or does the commonwealth count? Isn't the UK alone that same empire still, but evolved?