My first post here, I hope I've asked this question clear enough. I've read about several attempts made by the Byzantine Palaiologans to persuade western nations to help them against the Ottomans. State visits with gifts were meant to get support, and this was usually aimed at either Venice, Genoa, or the pope. Were western countries, or Europe in that case, the only hope for the emperors to escape downfall? Which countries or people could have helped them out? Did they try to request support from the Mamluks or other Islamic countries, or was that out of the question?
Actually there were also some supporters for Turks rather than West. For instance, Loukas Notaras, who was the last chief minister of the empire, said "I would rather see a Turkish turban than the Latin mitre in Constantinople.". As you can see, some devout Orthodox Christians strongly opposed the idea of reunification of West and East Church. So, they might have thought that living under Turks means the continuation of their Church.