MATH782 DESCRİPTİVE SET THEORY
| Course Code: | 2360782 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of the course, students are expected to have learned the basic theory of Polish spaces and standard Borel spaces at a level that will allow them to build upon further research related material.
Course Content
Topological preliminaries. Polish spaces, compact metric spaces, zero-dimensional spaces and Baire category methods. Measurable spaces and standard Borel spaces. Borel hierarchy, Borel sets and their regularity properties, and the Borel isomorphism theorem. Projective sets, analytic and coanalytic sets, and their regularity properties. Separation theorems. Polish groups. Selected topics: Borel determinacy, various uniformization theorems, theory of Borel equivalence relations etc.