MATH 592. Descriptive Set Theory.

Polish spaces; universality of the Hilbert cube, the Cantor space, and the Baire space; the Cantor–Bendixson theorem; Baire spaces; the Borel hierarchy; change of topology techniques; infinite games; analytic and co-analytic sets; analytic separation; the Luzin–Souslin theorem; the Borel and measure isomorphism theorems; regularity properties of analytic sets; uniformization; the projective hierarchy. Optional topics: Polish groups and their actions; definable equivalence relations and graphs; effective descriptive set theory.