Prove that at the end of the 13th century Byzantium finally lost its power
First, its territory has significantly decreased. The Byzantines almost did not control the Balkans, there were Slavic states – Bulgaria and Serbia. That is, during the period of the weakening of the Turkish states, the war was going on between the Orthodox, this mutually weakened them.
By the beginning of the 14th century, Serbia had become the most significant state in the Balkans.
Secondly, control was almost completely lost on the peninsula of Asia Minor, where the Turks were entrenched (the Ottoman dynasty dates back to 1299). Trebizond (Trabzon), where a separate state existed until 1461, fell away from it.
Third, the Byzantine Empire was economically dependent on the commercial republics of Venice and Genoa. They also had an influence on the shores of the Black Sea, for example, in the Crimea.