### Computable analysis and topology

Joe Miller, Spring 2018

This course will be an introduction to computability theory on metric spaces, with a particular focus on the

*continuous degrees*, i.e., the degrees of points of computable metric spaces. This degree structure (slightly) extends the Turing degrees and turns out to be a natural substructure of the enumeration degrees. We will cover essentially everything that is known about the continuous degrees, while taking interesting digressions into related topics, like the effective Urysohn metrization theorem and the noneffectiveness of the Brower fixed-point theorem. No previous computable analysis background is expected; a minimal familiarity with computability theory would be helpful.There is no required textbook.

semester:

Spring

prereqs:

Math 770, and Math 773 or concurrent registration in Math 773