SubjectsSubjects(version: 944)
Course, academic year 2023/2024
   Login via CAS
Descriptive Set Theory 2 - NMMA434
Title: Deskriptivní teorie množin 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 4
Hours per week, examination: summer 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 : NRFA072
Interchangeability : NRFA072
Is interchangeable with: NRFA072
Annotation -
Last update: T_KMA (02.05.2013)
Advanced topics in the clasical descriptive set theorey. Continuation of NMMA433. Recommended for master students of mathematical analysis.
Literature - Czech
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 - Czech
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (31.01.2022)

Zkouška má ústní formu s písemnou přípravou. Studentovi bude zadáno téma, ke kterému si připraví související věty, definice a důkazy.

Syllabus -
Last update: RNDr. Václav Vlasák, Ph.D. (09.05.2018)

1. Analytic sets and trees: Suslin sets and Suslin operation, Suslin operation and space of trees, Luzin-Sierpinsky index and coanalytic norms, Luzin separation theorems and principle of reduction.

2. Measurable uniformizations and selections: Kuratowski, Ryll-Nardzewski selection theorem, Jankov-von Neumann uniformization theorem, Michael selection theorem, projections and uniformizations of sets with large sections (in the sense of measure or category), projections and uniformizations of sets with small sections (countable, compact).

Entry requirements -
Last update: RNDr. Václav Vlasák, Ph.D. (10.05.2018)

Knowledge at the level of completion of Descriptive Set Theory 1 NMMA433.

Charles University | Information system of Charles University |