Why did Mehmed II call himself Caesar of Rome after conquering Constantinople?

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After conquering Constantinople in 1453, Mehmed II adopted the title Kayser-i Rûm (Caesar of Rome) because he viewed himself as the legitimate successor to the Byzantine Empire and the inheritor of all its historical lands.123

By capturing the city, which had served as the seat of the Roman Empire for centuries, Mehmed sought to resurrect the empire and extend it to its widest historic limits. This claim was reinforced by his efforts to transform the city into a worthy capital for a worldwide empire, as well as his strategic focus on subjugating territories in the Balkans and Anatolia, which he referred to as Rûm. Additionally, the Ottomans emphasized this Byzantine legitimacy by repurposing significant symbols, such as converting the Hagia Sophia into a mosque, thereby blending their imperial identity with the legacy of the Roman past.234