Descriptive Set Theory 1 - NMMA433
Title: Deskriptivní teorie množin 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Václav Vlasák, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NRFA071
Interchangeability : NRFA071
Is interchangeable with: NRFA071
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Annotation -
Last update: T_KMA (02.05.2013)
Introduction to the clasical descriptive set theory. Recommended for master students of mathematical analysis.
Literature -
Last update: T_KMA (02.05.2013)

KECHRIS A.S. Classical Descriptive Set Theory, Graduate Texts in Mathematics 156, Springer, 1995.

Requirements to the exam -
Last update: doc. RNDr. Petr Holický, CSc. (29.10.2019)

The lecture is concluded by an oral exam. Students will prepare their answers making remarks which could help them and

present definitions, theorems, and proofs related to the questions.
Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (11.06.2015)

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.

Entry requirements -
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (26.04.2018)

The student should have some basic knowledge about metric and topological spaces.