Syllabus
1. Polish spaces, the Baire space, the Cantor space, the Hilbert cube, the Hyperspace of Compact Sets.
2. Introduction to Borel hierarchy, basic relations in Borel hierarchy, closure properties, introduction to analytic and coanalytic sets, the Souslin scheme, the Lusin Separation Theorem, Borel injections.
3. Measurability of analytic sets, the Solecky Theorem, the Perfect set theorem for analytic sets, (non)regularity of coanalytic sets.
4. Introduction to infinite games, the Banach-Mazur game, the Choquet game, determinacy of games: closed games, the Martin Theorem, the Axiom of Determinacy, games and regularity, the Separation game and Hurewicz type theorems.
Annotation
Introduction to the clasical descriptive set theory. Recommended for master students of mathematical analysis.