I've heard that after the Muslim conquest of Constantinople the exodus from the city into Europe fueled the European Renaissance through the introduction of Greek texts and thought. We're these people in Constantinople utilizing renaissance level thought and technology prior to the exodus. If so What did this advancement look like?
In short no. But, also yes. At the time prior to the Muslim conquest the Byzantine government was to weak to properly tax its people. Because of this there was much more money around to be used for the patronization of the arts. As such the remains of the Byzantine empire went through a cultural Renaissance. There was a massive resurgence in art and literature, as well as a resurgence in theological debate (1). There were no great technological advancements, but rather a rediscovery of the idea of Classical Greek culture. To accompany this was the public school of philosophy, and the patriarchal school (2). the Fall of Constantinople had a negligible effect on the Italian Renaissance as most of the Greek scholars who brought their texts and knowledge to Italy did so in the 1300's (3).