Summer Research Scholarship - Degree Structure of Computable Presentations of the Unit Interval

This is a Summer Research Scholarship project offered through Victoria University of Wellington's Summer Research Scholarship Programme. The project focuses on investigating the degree structure of computable presentations of the unit interval in computable analysis. In classical analysis, topological spaces being equivalent up to homeomorphism forms an equivalence relation. However in computable analysis, the computable homeomorphism relation induces a preorder on presentations of the space, which is not well understood even for simple structures like the unit interval. The research will investigate this degree structure to better understand its computable presentations. This is a single-student project supervised by Dr. Sasha Melnikov, Associate Professor in Mathematics at the School of Mathematics and Statistics. The project will be conducted mainly at the University's campus locations in Wellington.